If it's Bruce Wayne vs. Steve Rogers, Steve Rogers all the way. He'll easily outlast any normal human with his augmented stamina.
If it's Batman vs. Captain America, Batman all the way. Bats has numerous gadgets in his utility belt that don't have to strike Cap to neutralize him.
Batman cheats, and blah, blah, blah, but Cap would whip him.
Oh and why? Cap has fought people with plenty of gadgets before. I think his "will to" would get him past Bat's devices. Kind of like intangibles they always talk about in sports.