For me, Batman Returns is unquestionably the best of all the Batman films - and yes, I'm including both The Dark Knight and Dark Knight Rises when I say that. Burton's first movie had awesome moments but relied too strictly on blockbuster conventions to elevate it beyond just another action film. Both Forever and Robin are categorically terrible. Batman Begins has the same problem the first Burton Batman did, and both The Dark Knight and Dark Knight Rises, while very good movies in their own right, have a unique problem: Batman is actually the least interesting character in those movies.
What makes Batman Returns so different is that it's creative. From what I understand, Burton didn't actually want to make another Batman film unless he had full creative control, which he was given. The movie that resulted is quite weird. The characters of Batman Returns are less realistic than the characters in Batman: The Animated Series, which is saying something. There are jokes here on par with the '60s Batman: The Movie in terms of unbelievability, yet Returns remains strikingly dark.
Where Christopher Nolan basically just tries getting away from Batman's tropes to make a more "realistic" movie, Burton embraces them and makes them his own. If nothing else, Batman Returns is the only Batman film with a true, unique interpretation of Batman. Burton's Batman never broods, but he carries a gun (like the original) and even kills a few guys. There aren't a lot of questions as to WHY he remains Batman, a theme that is central to practically every Batman film that comes after this. He just is. It's his job. He even cracks jokes now and then ("Eat floor. High Fiber.").
More than anything, I like Batman Returns because it is operatic. Danny Devito's Penguin, which is at least as terrifying a transformation as Heath Ledger's Joker, is a disfigured psychopath, yes, but in a way he's also a really pitiful character. He's caught between an obsession with revenge and regaining his family name. Though his public persona is clearly a put-on thing, it's at least interesting to have a villain who isn't just yet another redefinition of what is pure evil. There is a scene where he finds the gravestones of his parents, falls to his knees, and raises his arms towards a cross in the foreground. He does this not because he's feeling genuine anguish, but because there is a crowd watching and he's a master manipulator. He's performing.
There's also some satire here, too, and the deaths of the villains are some of the most visually striking, spectacular deaths I've ever seen in a movie. Danny Elfman's score is masterful, better even than the previous film, which had a main theme that I'd easily put beside John Williams Indiana Jones theme in terms of quality. There are insanely cool, massive sound stages that impress sheerly because of their size and design. Michelle Pfeiffer's Catwoman is a big part of what makes this movie so unique because she ties both villains and the hero together in such a way that keeps things feeling connected and interesting. The other villain, who I have yet to mention, is Max Shreck, who is impressively evil as played by an unhinged Christopher Walken.
Maybe Batman Returns is not the Batman you expect or even necessarily want, but it's certainly the most complete vision of the character yet to be put on film.