I want to talk a little about the differences between Hit and Jiren.
I've heard people say that Jiren is just a more boring copy of Hit, which isn't totally unfair based solely on the anime. I think the manga does a much better job of making these characters feel different. Yes, both are somewhat stoic, bad-ass, bald rivals to Goku, but what drives these characters is completely different.
Before the Universe 6 tournament, Hit was an assassin. As a 1,000 year old individual, he had likely been assassinating for quite some time. Whatever the reason for getting into assassination in the first place, it's something that he stuck with. He didn't continue to do it due to a lust for killing. He didn't continue to do it for the money. He did it because he was good at it. Nobody could challenge him, and it's likely that nobody had in centuries. He didn't find assassination thrilling at this point, but it's all he knew how to do anymore. He was bored.
When he agreed to attend the Universe 6/7 tournament, he did it on the condition that he would be given the Cube Spaceship if he participated. It's never stated as to why he wanted the spaceship, but I'll get into that later.
Once the tournament had started, Hit proceeded to sleep up until the point where Vegeta went Super Saiyan Blue. Hit was so far above everything else that had happened up until that point that he wasn't even interested in the tournament for the sake of sport. Vegeta Blue gave him hope that he might find a challenge, but Hit quickly disposed of him as he would have any other target. He was so let down by this that he asked the ref if he should throw Vegeta's unconscious body off-stage just to get the tournament over with.
Once Goku appears on stage and starts revealing his strategy immediately, Hit knows something is different about this contestant. At first, he's inclined to think Goku is simply stupid, but when Goku suggests he's gotten a hint as to how to defeat Hit, we get this
devilish grin. Fuwa mentions that Hit - a person who never talks - is becoming quite chatty with Goku. Hit is grinning, sweating, and put on edge.
Eventually, Goku takes the edge in the battle. Hit can't believe it, but even then he smiles. When he powers up to max and is able to stop SSG Goku for a moment, the expression on his face is absolutely ecstatic. All he did was manage to stop Goku for a fraction of a second, but the look on his face was completely different from when he actually defeated Vegeta.
We know the rest. The point is, despite seeming totally detached from the tournament initially, Hit loves battle. He had grown incredibly bored at the top in his universe (similar to Saitama in One Punch Man), but Goku showed him that there was still plenty of room for him to improve. Now, we never hear exactly why Hit wanted the Cube Spaceship, but based on his battle with Goku, and based on the fact that he gave up on the Cube immediately after taking the fall against Monaka, it seems that Hit wanted the Cube in order to seek out a challenge. Now that he had his wish granted another way, it was time to get to training.
Upon seeing Goku again at the Tournament of Power, he plays it cool for a second, only to relent a grin and say "Do you really think I've been sitting on my hands since the last tournament?" Goku replies "Great! Should be fun" with his own challenging grin. They exchange similar chemistry throughout this most recent chapter. When Hit asks Goku to team up against Jiren, but Goku refuses, he's confused at first, but not frustrated. He doesn't berate Goku for making such an irresponsible decision, but rather, he smiles as he realizes that was the "right" answer all along.
We know from the anime that all universes would be destroyed if the winner of the Tournament of Power didn't wish for the revival of all universes, and if Hit had been the last man standing, I'm certain that he would have made the right wish in order to continue challenging himself.
While Jiren is quite stoic and quiet as well, I don't get the sense that he is as bored as Hit. At the very least, he has a sense of purpose. He is certainly on top in his universe - above the God of Destruction even - but he has something he actively pursues on a daily basis. Whether or not he has fun doing it, he cares deeply about justice. He wants to ensure that he lives in a just world, and knowing that he can do something about it keeps him moving non-stop. The idea of attending a 48 minute tournament that MIGHT allow evil to go unpunished for even that long sickens him. Having seen the anime and read developer interviews, we know that Jiren's hunger for justice is motivated by what happened to him growing up.
If Jiren had an interest in becoming Universe 11's God of Destruction, he could do so in an instant. Like Goku, he's uninterested in the job. Both characters don't want to be burdened by the responsibility because it would get in the way of doing what they love. The prestige of the position is meaningless to both of them. When Jiren hears that Goku and Jiren share this sentiment, it grabs his attention. There is nobody else in his world that thinks in that way. Toppo wants the position. The rest of the Pride Troopers are just a rag-tag team of fighters assembled for a job. Nobody, not even Vermoud understand why his purpose is so important, but perhaps Goku would. It's not that Goku actively pursues justice, but he would understand the idea of doing anything to accomplish your goals. While Hit would also likely be uninterested in the prospect of becoming a God of Destruction, his role as an assassin inherently makes him less suited to the position than do-gooders like Goku and Hit.
While Hit is a very passive character when he meets Goku, Jiren is very active. While he's not interested in the prospect of the tournament in itself, he wants to get the battle over with so that he can go home and continue enforcing justice and peace. Even if the World of Void is outside of time, the time passing in Jiren's head is constantly reminding him of his true objective. The anime does little to support this when they have Jiren in a meditative state for half of the tournament.
There are many things we still don't know about the manga's incarnation of Jiren. Does he love to fight? What is the wish he wants granted? How will Goku affect him moving forward, and vise-versa?
For the sake of speculation, let's assume that Jiren's wish is to revive his loved ones that were murdered over the course of his lifetime. If the Super Dragon Balls were awarded to him at the end of the tournament, would he have made the right wish? We know that Jiren doesn't want to be responsible for the destruction of other universes, but he agreed to join the ToP despite that under the assumption that he would be able to have his wish granted. While he may have changed his mind by the end, it's entirely possible that he would have misused the wish and ended up erased.
TLDR;
Hit: Passive // Jiren: Active // Goku: Active
Hit: Motivated by Battle // Jiren: Motivated by Justice // Motivated by battle and his loved ones
Hit: Unaffected by murder or evil // Jiren: Cannot abide evil for even a moment, refuses to kill // Goku: Hates evil but does not go out of his way to punish it
Hit: Typically calm but electrified by his passion // Jiren: Pursues his passion intensely but calmly // High energy despite not constantly seeking social interactions, electrified by his passion
Hit: Doesn't hesitate to accomplish the task at hand but will enjoy a fight above all // Jiren: Accomplishes the task at hand so he can get back to his true mission // Goku: Seeks to enjoy a challenge at great risk up until the point of hopelessness, but does the right thing in the end
Hit: Would restore all universes // Jiren: Might not restore all universes // Goku: Would restore all universes
Hit: Changed by Goku // Jiren: Will be changed by Goku // Goku: Goku
While I may have gone in-depth into the mental state of these characters just now, we know of course that Akira Toriyama would never explain emotions so blatantly. It's not his style. That being said, just because a character doesn't explicitly say something, that doesn't mean that the point isn't still getting across somehow. That's the genius of Dragon Ball; it's able to keep things light on the surface while still allowing you to dig deeper when you're thinking about it later.