Let me put all the speculation to an end.
Batman is the master of a BUNCH of styles but that does not make him a better fighter than cap off of pure h2h, Cap has shown that he can throw down with the best of them and win, cap has Taken all the EFFECTIVE martial arts and mixed them together, making him ATLEAST batmans equal if not his better, MARVEL has stated that cap is probably the best unarmed combatant that the world has ever known.
Cap is also batmans superior physically by great amounts, he used to be able to lift 800pounds when he first came out, but has been seen to press slightly over 1,000pounds, he can regualarly curl 500pounds contiously and over multi reps in work outs, and has the best stamina any human could ever have, his body can operate at full speed for hours at end.
If this battle is pure h2h, the cap wins, and pretty fast, his judo is better, his jiu-jitsu is better, he trains more, has more experience, and his physically better. this fight doesnt last very long at all
The cap by way of beatdown EARLY 10/10