In my opinion, while you do have to deal with the differing styles of Christopher Nolan and Tim Burton, you also have to realize that contextually, Batman is a character that has been all over the radar since his inception.
The Batman of the '30s and '40s was far more gritty than the character of the '60s and '70s that most people grew up with. In that sense, Burton's Batman was a more serious look at a less-serious Batman, directly influenced by the Silver Age comics and (fortunately or unfortunately) the original film and television program. Burton was happy to allow the characters to be a little campy, but you could see the gritty look and feel that the comics had been taking bubbling under the surface. That really became evident with Batman Returns, which in my opinion, was the film's downfall. That is not to say that the film was bad, but more or less, that people (in general) did not want to deal with a gritty version of Batman with serious problems. The Schmacher films were a reaction against that.
By comparison to Burton, Nolan had the advantage of time, and the ability to stand upon the writing from Miller, Moore, Loeb and even the production work by Bruce Timm. The '80s and '90s fleshed out Batman as a human being, and gave each character a very distinct reason for being who they are, and doing what they do. The Joker went off the deep-end compared to what he was in the '60s and '70s, and with characters like Hush, Bane and Zsasz, Batman was brought down to a very complicated, brutal reality. In my opinion, that kind of evolution is where Batman belongs, dealing with the cereal serial killers, psychopaths, mass-murderers and terrorists... Things we deal with in real life. It really is a matter of thinking of things just as Nolan did when making Batman... If someone really did want to go out and do this, what would be the ramifications? How would people handle it? What would come of it? Part of it as well has been that the sensibilities of Americans have changed, and that our sensibilities are drastically different as well. The violet, senseless acts of The Joker in TDK are far more believable than what they would have been 20 years ago in Batman.
I feel as though Batman is a character that comes around every once in a while to accurately reflect the way people were feeling, or wanted to feel. The Batman of the '30s and '40s fought against organized crime and corruption that eroded our society so much during the Great Depression. The Batman of the '60s and '70s was an escape from the horrors of Vietnam and and the social conflicts at home. The Batman of the '80s was a response to the Regan optimism, and the threat of nuclear war. The '90s and '00s have been a nexus of events for Batman, and in the end, you get to pick your poison. Between the films, comic books, television programs, and even the videogames... You see a dramatically different character that deals with similar issues in completely different ways. While my version of Batman was greatly shaped by Bruce Timm's Batman: The Animated Series, I feel as though Batman: Arkham Asylum and TDK are the best representations of a "modern," "realistic" Batman.
I haven't seen them in years.
