
The Legendary Super Saiyan Form, in the context of the greater story is an incredibly deep critique of the saiyan race at it's core. This form is deemed as the ultimate representation of a Saiyan's power. While we do not know how the new representation of the form will play out, it carries many similarities and so this will be written based on what we have seen of the previous versions of it.
1) Power- The form is incredibly powerful, far stronger than the strongest organic being in the universe which was Frieza. We really have no idea quite how strong the form is, but if we compared it to say Cell, I doubt Perfect Cell could have handled all the Z warriors simultaneously, and certainly not as effortlessly.
2) Sadistic Nature- This is perhaps the most important aspect. Saiyans, up until Dragonball Minus, were evil and sadistic in nature. In the same ways that the LSSJ takes the saiyans' natural power to its MAXIMUM

In this way the LSSJ is not a true character, much like the Hulk is a deeper critique of what dwells inside men. LSSJ is more akin to a force of nature and the Saiyan race personified by it power and cruel evil nature. The character Broly, being merely a vessel for this raw force to act through.
Why does this make it a masterpiece?
First and foremost the SSJ transformation was a form Vegeta prided himself on believing he was destined to achieve. While he eventually achieved it, it was after he believed Goku had obtained it. Once the realization that he could also obtain it, he believed he would be the strongest saiyan alive. During this particular time period Vegeta still heavily embraced Saiyan nature and tendencies, he valued strength and brutality over the love and companionship which Goku embraced as a saiyan. In fact when he was told by Paragus that there would be a New Planet Vegeta, Vegeta jumped at the opportunity to once again embrace and establish his saiyan heritage.
However, when he came face to face with the true raw nature of Saiyans he cowered in fear. The raw unbridled Saiyan power and rage, the very nature of saiyans personified was even enough to terrify the Prince who celebrated the power and cruelty of his own race. It was the first time, in my opinion, that Vegeta saw saiyans and his race for what they truly were.
As a Vegeta fan this is my favorite clip
https://www.youtube.com/watch?v=cHpkDnOZtCY
Further it took Goku, the only full-blooded saiyan to completely over come his natural saiyan tendencies to fight the raw personification of his own blood. The fight was far more symbolic in that Goku was fighting a part of himself, he was literally fighting the full personification of what was inside of him and not only did he reject it, but he was able to overcome it the same way he first overcame his saiyan heritage as a child, with the support and companionship of those around him and for a purpose greater than himself.
So, in conclusion. The LSSJ and its fight represent a far deeper critique of the saiyans with far more personally meaningful aspects to the characters then any fight I've ever seen in Dragonball. It causes Vegeta to pause and question his very nature of what he's reveled in, it shows a physical representation of the struggle Goku endures as he fights against his very nature. It appeals of so many layers and often feels lost on the vast majority of the fandom. This is of course my opinion but greater significance of what this particular struggle represents for the characters is far more interesting and emotionally charged to me.