Its a tough call. The Burton films are good, but they aren't really about Batman.
I felt this way too up until a few days ago, but after Googling a lot of stuff its turns out that its not so cut and dry.
Some things I didn't realise for instance were that Catwoman's original origin was that she was a normal woman who accidentally smacked her head hard and had a complete personality change as a result, and there's a Penguin story where he straps rockets to penguin's backs (albeit they're duds in this story), Penguin running for mayor is an homage of one of the Adam West episodes.
Batman 89 is actually very, very accurate, but its almost wholly based on Golden Age Batman from the 40s, the only major change they actually made was to merge the Joker origin with Batman's (which the writer later said was done against his will when he was absent), everything else actually follows the first 40 issues quite closely at times.
An argument can be made that
Tim Burton Batman = Golden Age Batman
Batman and Robin = 1960s Batman
Batman Forever = 1970s Batman
Nolan Batman = Contemporary Batman (mainly Jeph Loeb + early Frank Millar)
You know I never made that connection, but you're quite right. The way the characters interact with eachother, the way Batman kills, the enemies he fights..... it's all very similar to the early Batman comics. I've only ever read 2 Batman comics from the 40's, but thinking about it now they weren't dissimilar from the '89 film.
I wonder if that was a decision Tim Burton consciously made. He said he didn't really read that many Batman comics, but he was probably given a bunch of them from DC.