As an ex-regular peruser of vs. threads, I've never seen this particular one.
Of course, Batman's advantage in a fight is his half-hour of prep. With that, we know he can beat just about anybody.
No prep? Depends on the environment, of course. A more acrobatic or dark environment, Bats has stealth and movement in the bag. Clean fight in a flat dojo? I'd probably go with Cap, but I could see Bats taking it.