EDIT: I also included Buu arc Vegeta.
Vegeta was content with his position as a Saiyan, seeing as how he represented the pinnacle of the Saiyan race. The main thing about Vegeta is that he defines himself by his pride and had more pride than the average Saiyan since he was more pleased with his position and the societal hierarchy beliefs. Because of this, he shows even less compassion than the average Saiyan and puts down others to satisfy the ego his pride and upbringing created. This was shown when he was first introduced, instantly turning down bringing back Raditz which Nappa suggested because of Raditz inability to meet the expectations Vegeta's outlook on life placed on him, by not defeating warriors with lower fighting powers. Because he values what he was brought up to believe more, he judges others sorely on his belief without a shred of compassion.
His belief in hierarchy and the Super Saiyan legend made him believe that he's the only member of his race (And the only person in the universe) who can potentially restore the pride of his race and himself by defeating Frieza. The Saiyans dying didn't bother him much since they were only an extension of his own pride, even in death. But when Goku bested him via Kaioken x3 in the Saiyan arc the thought crept in that none of what his grew up to believe in is true, and that his position as prince, the source of his pride, doesn't mean anything since his race is gone which would force him to swallow the weight of his comrades death without having his pride to protect him from feeling compassion, and that he'll forever be a slave to Frieza without any chance of restoring the pride Frieza slowly depleted from him. That - Which stemmed from the humiliation he felt from being outclassed by a lower class was a thought he could not endure. It gave Vegeta a taste of what it'd feel like to not depend on his pride, a feeling which he hated. His encounter with Goku made him more concerned with his pride, as shown by him showing concerns about being Frieza's slave for eternity if Frieza achieves immortality rather than only caring about fighting forever. He never experienced any feeling of compassion beforehand because of his pride, which made it harder for him to handle those feelings than the average Saiyan.
Although Vegeta was content with his position, he was still serving under Frieza. This was an insult to Vegeta's pride that he could barely swallow due to the immense potential the Saiyans and himself believed they had (i.e Zenkai Boosts and Super Saiyan). It was the greatness of what the Saiyans could be as the best warriors in the universe that filled him so much pride even with Frieza damaging it by enslaving him and degrading him by regarding his race as nothing more than savage monkeys and lower lifeforms. Frieza enforced the idea of Saiyans not having any more worth than the scouter's readings project into them to avoid them thinking to rebel, but thanks to Goku beating him, Vegeta looked beyond it by not relying on his scouter, a representation of his outlook, to judge others and himself and that he can do more with his Ki and thus had even greater potential than his upbringing led him to believe which allow him gain the upper hand on his superiors despite being weaker than them. Vegeta was happy with the alteration to his initial outlook despite it taking his pride being wounded by a lower class to have it, especially since he was able to put down those who would once put him down with said initial outlook by mocking their reliance on scouters.
Vegeta and the others Saiyans hated Frieza because of how prideful they are, and hate for taking orders. The fact that the same Frieza destroyed their planet meant that Vegeta needed to defeat him all the more for his pride's sake. Vegeta's death on Namek was a great way to set up for their rivalry because of how devastating it was for the character. Such devastation that no other Saiyan in history had which is key to the events that proceeded it. The fact that not only did a lower class warrior humiliated him, but he became the legendary SSJ and defeated Frieza and even begged said lower class warrior to defeat him, damaged his pride to the point that he needed to defeat said lower class warrior to restore it. But at the same time he was glad that a Saiyan was able to defeat Frieza, otherwise it would've been impossible for his pride to ever be restored. However, since Goku still defeated Frieza his pride was still very damaged. It was only less damaged than it would've been if a Saiyan didn't defeat Frieza.
During the end of the Namek arc Vegeta came up with the idea for Goku to be wished back, claiming he only wants him alive so that he can have the pleasure of taking down the legendary Super Saiyan himself. This marked the genesis of Vegeta's obsession with Goku, from wanting to rule the universe and thinking of him as nothing more than lower class scum to a lower class scum who became the legend itself and his ultimate objective. The events of Saiyan/Namek arc made him no longer care about immortality and conquest and focused solely on beating Goku with his own hard work alone for the sake of his pride.
The big difference between Goku and Frieza in terms of Vegeta's desire to kill is not only how Goku devastated his pride more than Frieza did, but the fact that Goku is suppose to be a lower class of the same race whereas Frieza was at the top of the inter-galactic food chain with the entire Saiyan race being below him which made it naturally easier for Vegeta to accept that Frieza was above him. But the fact that a lower class warrior was Vegeta's main goal and is now the Legendary Super Saiyan and was above him was harder for Vegeta to stomach, since strength in Saiyan society was defined by the hierarchy.

Witnessing Trunks and Goku as Super Saiyans with his own eyes fueled his desire to surpass Goku even more. He couldn't stand to see these two Saiyans achieve something that Vegeta himself, who was at the top of the Saiyan hierarchy, should achieve first/before them. Especially Goku. Because of this, Vegeta's training methods were fueled by his hate for Goku and his need to surpass him and reclaim his position as the Prince of Saiyans. From that point on, whenever he trained he primarily focued on how to best Goku's own training/strength not to just surpass the main villains the Z-Fighters were up against. This was shown by his decision to train at 300x earths gravity in response to Goku training in 100x earths gravity.
"Does a Machine like yourself ever experience fear?" Undoubtedly one of Vegeta's most badass quotes but I think I managed to uncover the deeper meaning behind it that makes Vegeta's character development even better:
It showed that when Vegeta sees the Androids he sees the reflection of what he could've been if still under Frieza's rule and still followed his empire's outlook on life, that one's value is entirely set in stone by numbers and statistics making followers of said outlook nothing more than machines and how Vegeta's fear of being limited by that outlook produced what he believed to be a better outlook than those who are content with it. By not seeing past numbers, Vegeta felt people like Dr. Gero will always be inferior to him because of their lack of concern for the limits their outlook on life placed on them.
Vegeta was right too, by being content with his numbers Dr. Gero convinced himself that he was being cautious by having contingencies (i.e backup Androids and Cell) similar to how Vegeta allowed Frieza to make him content with being an Elite Saiyan (And in turn other Saiyans being content by having pride in their race due to the elites existing). But, unlike Vegeta who at one point feared his pride being depleted by Frieza's empire enforcing the idea that Saiyans will never be greater than the scouter readings which goes against the Super Saiyan legend, Dr. Gero didn't think to wait until Cell is completed and absorbed the androids before attacking Goku which would've led to his victory because he didn't feel himself or Android 19 could be defeated, that lack of fear was what led to his downfall unlike Vegeta who became the Super Saiyan his initial outlook would've denied him
Although Vegeta's pride is what defined his character and was what pushed him forward, his pride in being the Prince of Saiyans also was his detriment compared to Goku's more humbled nature. This is shown when he finally achieved Super Saiyan. He achieved it by stressing his body through the most rigorous training imaginable (As well as his frustration in reaching his limits) during the 3 years, the mental and physical stress that led to him becoming Super Saiyan as well as him becoming a Super Saiyan affected his mentality even more. He was content was the SSJ transformation and was more arrogant than ever in the entire series, some people may have hated Vegeta during this portion but to me it was a significant part of his character development.
It was understandable for him to act as he did because finally became the legendary Super Saiyan after Goku had been haunting his mind during his years of training to become a Super Saiyan, not to mention the fact that the Super Saiyan legend itself was touted to be the strongest form in the universe. Individuals who stressed to achieve something tend to have more pride in their achievement, and with someone who defines himself by his pride like Vegeta who achieved the biggest achievement a Saiyan could achieve at the time, you could almost expect him to act as arrogant as he did. Trunks' predictions were also proven wrong so Vegeta had a reason not to believe Trunks when he said he'd die fighting the Androids. Vegeta at this point needed to ignore Trunks warnings. He needed to believe that he is the strongest in the universe for his pride and since there was a chance (As slim as it may be) for Trunks to be wrong, it made sense for Vegeta not to follow his warnings. It took 18 beating him to realise Super Saiyans aren't invincible, and for him to aim for something greater and not let his insecurities stop him from doing so.
Another example of how his pride was a detriment was his belief that as long as he's at the same level as Goku he'll always be superior and will be able to finally kill Goku. This is why he was so content with being a Super Saiyan as well as Grade forms. He mainly sees someone surpassing him as a loss.
I think the part that gives a really good insight on this element of their rivalry was when Vegeta wondering why Goku wouldn't be pissed off about someone surpassing him after doing so much hard work to obtain greater powers. It highlights the difference in their mentality that makes Goku better than Vegeta. When Vegeta works hard, he does it because of his desire to kill Goku and become the strongest, because he cannot stomach the idea of someone being better than him. He works hard so he can be content with his achievements. He loves knowing that he's the best and that no one can surpass him, especially since him being a Super Saiyan elevates him to the top of the inter-galactic food chain in his eyes. Whereas, Goku works hard because he enjoys the hard work, he strives to better himself not only to better others, which is why he loves the prospect of someone surpassing himself because he loves knowing that there's a limit he has to overcome and hates the idea of being the strongest. The Android arc was the only arc when the difference in their powers were sorely because of their mentalities, which is why their rivalry was done in the best way in this arc.
This also reflects on their attitude towards receiving help from others. Goku humble upbringing and pure hearted nature led to him having assists from others in his quest to become stronger. But Vegeta "Survival of the Fittest" mentality led to him not caring for others and thinking others would just slow him down. This is reflected with their sons. Trunks was supposed to have greater potential than Gohan, but Vegeta's lack of care for him as well as his own mentality when it comes to training in comparison to Goku made Gohan stronger. His anger towards Goku fuels him, which was why he couldn't possibly achieve the MSSJ due to the requirements of the form to be in a relaxed state within the SSJ1 form. Although Vegeta is a better genius than Goku, his anger clouded him from thinking of the MSSJ since the initial SSJ form was based on anger.
But the main thing that really adds to the greatness of Vegeta's character was him deciding to give up fighting due to Goku's death. It shows that Goku truly became the core of Vegeta's pride. Goku became the thing that defined Vegeta's will to fight because he practically took his pride from him by his actions up to this point. Vegeta couldn't lived with the fact that he'll never be able to kill Goku himself and reclaim his pride (The most important thing in Vegeta's life) and couldn't go on because of it. He'd probably even have been suicidal if he didn't have a son to care about, who he only cared about because Goku died along with his pride (He cared for no one due to his pride, like all the other Saiyans). He's the only Saiyan to have had his pride shattered like this. The Vegeta who was after Frieza wouldn't care as much if Frieza died, and would still aim to rule the universe. But the Vegeta in the Android arc was so wrapped up in his hatred for Goku that he couldn't go on without him by the time Goku died. This was a great dynamic between them because Vegeta throughout the series up to this point was still pure evil because he still had his pride and could've been a potential threat to the earth with it, while Goku's reasoning for staying dead was he believed the earth would be safer without him due to bad guys being attracted to him throughout his life. Vegeta needed Goku.
Vegeta desperately wanted to retain any fragments of his pride by not wanting to receive help from others more than ever and training in the most stressful way imaginable during the Android arc because of Goku. Vegeta claims to not care for the Saiyans and his family on a emotional level which is true, but only true because, like other Saiyans, his Saiyan nature prevents him from feeling compassion. His pride shielded him from having to face the major loss he had at the hands of Frieza the entire time because, deep down, he and other Saiyans have a speck of compassion. It took Goku completely shattering his pride by staying dead for Vegeta to face his losses and forced him to rely on said speck via caring for his family in order to have the will to live, which made him a depressed man. Vegeta's decision to stop fighting and care for his family added to his previous developments (i.e his reaction to Goku besting him in Saiyan arc).
When Vegeta went Majin he knew it was his only chance to beat Goku. Babidi's spell didn't work on Vegeta because, like Vegeta said, pride is the one thing that cannot be taken from a Saiyan, the same pride that shielded Vegeta's mind from his losses. At this point in Vegeta's life, it was no longer about proving that his beliefs as a warrior are better than Goku's, it was about regaining what pride he has left from the man that took it from him. Thanks to Goku, Vegeta was left broken and actually had to bond with his family. Something that Vegeta believes only weaklings do. Vegeta was forced to go against what he believed makes a strong man merely to have the will to live. But after reflecting on what he's become, he realised he's become a better man than before, he reached a level far beyond many Saiyans throughout history and although he didn't reclaim his birthright, he was lucky to have someone like Goku regain the pride of the Saiyans for him by defeating Frieza. And although it hurts him, it was Goku making him look beyond social statuses in Saiyan society that moulded Vegeta into a better warrior than he would've been otherwise. If he wasn't inspired by Goku to work on his senses and ki control he wouldn't have went as far as he did on Namek, giving him what he believed to be a better outlook on life than Frieza's empire. If it wasn't for Vegeta's desire to become better than Goku he wouldn't have become as strong as he is now, and if it wasn't for Goku deciding to stay dead he wouldn't have taken the time to bond with his family and have something to fight for other than himself. Vegeta realized that, as much as it hurts him to admit it, Goku moulded him into a better man and Vegeta himself is thankful for it. Hence why he sacrificed his life for Goku as well as his family because in a way, Goku was Vegeta's most important friend.
People believed it would've been better for Vegeta to have called Gohan instead to kill Kid Buu, I think even Vegeta realised it too. Vegeta's real reason for suggesting Spirit Bomb against Kid Buu was for his pride. He was trying to have pride in his new people, similar to what he had for the Saiyans by having them achieve something grand by contributing to Kid Buu's defeat. This was the only way Vegeta's pride can be regained to the point that he didn't need to defeat Goku, which allowed Vegeta to come to terms with the fact that he cannot be better than Goku. He realised at this point that Goku was his true inspiration, and although he was a better warrior than ever thanks to Goku, it was Goku's level of purity that inspired him, a level of purity that Vegeta admits that he can never reach. Which is the key difference between Goku and Vegeta and why Goku is "Number One".

So, what do you guys think?




