The Superman matchup is also tough. His zoning works very well against Batman`s long dash, and f23 outranges everything we have in footsies; Granted we have trait bats to get in, and to whiff punish and stuff, but he can do all that easier than us, for free. And he has better air mobility and DAT corner damage...
He is the best character in the game, at least in my book.
(And yes, I am salty LOL)
Edit: Also, I must say that the DoomsDay matchup is not bad for Batman... DD can be insanely overwhelming if you let him gain the momentum, but after playing him a lot, I think it`s even. You have to be in control of the pace, you have to pressure him. Batman`s normals are faster than DD`s. Play calm, study the frame data, and don`t let him get you in the corner.