What bothers me about the Burton films is that Bruce and Batman never have an arc. He's the exact same character at the end of Returns as he is at the beginning of Batman. Things happen to him (he discovers, and then kills, his parents' murderer; he falls in love twice), but he never learns a lesson or evolves.
At least Forever takes a stab at reconciling the murdering psycho from the first two films with the newly super-heroic version, and B&R has Bruce accepting Robin as an equal (and some bullshit about family).
Burton's Batman is also highly indifferent to the people he's saving. The Burton films are highly cynical in their portrayal of the yuppies of Gotham. Why does Batman fight for these people? They're selfish, idiotic, and vapid. It could be that he's only out for vengeance, but then why give the police the Batsignal?
The Schumacher films at least portray a heroic Batman. Simultaneously, they also subvert the audience expectations of what's expected out of a Batman story, superheroes in general, and a movie based on a comic book. Grant Morrison's JLA started in 1997, the same year as B&R. Although Morrison has done a much better job in the last fourteen years of respecting Batman's entire publishing history and making the sci-fi/camp eras work, B&R at least takes a stab at reversing the grim & gritty portrayal of superheroes, and Batman specifically, that was started by The Dark Knight Returns.
In the end I don't think the first four Batman movies are really all that good, but as I get older I have more fun with the latter two. I say skip 'em all and rewatch the Nolan films, or better yet the Animated Series.