Good GOD this is tough... Okay, here's the thing for me:
Danny Elfman... is probably one of the greatest composers alive. And he did wonders for Batman, just like he did for Spider-Man. In many ways, he did make the
Batman theme and the music is astounding in those films. "Finale" and "Descent into Mystery" are breathtaking, some of the best music composed in film.
Hans Zimmer/James Newton-Howard - They might just be my favourite. I wasn't really old enough to ever see the Burton films when they came out (I was barely alive for Returns, actually) so I very-much view the Nolanverse as MY Batman series, and the music I strongly remember and even hum to myself a lot. Molossus? "Dun, dun, dun, dundun". It's great, I especially like the music that plays in the first and third films http://www.youtube.com/watch?v=V94K2eJnuCA
(right after he leaps into the swarm of bats to the end is what I'm talking about). That to me is the Batman theme of this series.
Shirley Walker - To me, that little piece that plays throughout Mask of the Phantasm and the animated series is THE definitive Batman theme. http://www.youtube.com/watch?v=TOSS-ZFDMo4
But I'll acknowledge that it's very Elfman inspired and it's very small.
EDIT: I also REALLY loved the Clayface theme and the music from the "Captain Clown" episode.
Tough call, but I'm going to go with Zimmer/Howard. Which at some level makes me feel dirty. Maybe it's because I kinda grew up with the Raimi Spider-Man movies, but when I see people talking about how they prefer the Horner score from TASM over Elfman's masterpiece, I just feel vitrol, because it's such an inferior score. Maybe that's also because I hate how everybody leaped onto TASM's dick as soon as it started coming out because it was easy enough to buy people with a Spider-Man that used mechanical webshooters and dated a blonde-chick first. I don't know, I'm just going with Howard and Zimmer.