I could see the Nolan/Bale Batman being actually Slytherdor. A lot of the trilogy (especially Batman Begins) deals with courage, bravery, fear. Also, he is not that much of a researcher himself, mostly lets Lucius or his Butler do all the detective work.

Whereas the more stereotypical Batman from the comics and games is rather Slytherclaw.

Not sure about the Ben Affleck Batman. He does seem more Slytherclaw, though.

Now the Batman from the 60s TV series is definitely not Slytherin. More like, Huffledor.
He is entirely different from the typical Batman persona.