Batman most certainly had the same growly voice in Batman Begins and The Dark Knight. It's more noticeable in The Dark Knight because Bale somehow manages to get more growly with it than in Begins, and Batman himself (not Bruce Wayne) has more dialogue in The Dark Knight, so there's more time to notice the way he speaks.
I just hope they bring it back to Batman Begins levels for the new movie, because I didn't mind it so much then.