The newest incarnation of the Dark Knight fights one of the most acclaimed versions. I insist on BTAS feats only, because TNBA/JL Batman would more than likely be too much for Batfleck at this point.
1.H2H
2.With standard gear.
Bonus: They sit and talk. What happens? For that one, you can pick whatever version of DCAU Batman (TNBA, BTAS, heck even Beyond) you want.