It's strange that people would list reasons why Captain America would win, but for Batman there is none. Batman doesn't win "because he's Batman."
OT: Batman has two ways of going at this. Either taking Captain silently using his training as a ninja, or by direct combat. Since Captain America has reflexes that have been honed to almost superhuman levels, I doubt a slow and silent approach will help, so close-combat is the way to go here. Captain America has shown mastery of a few different styles of martial arts and formed his own type of hybrid combat form out the ones he mastered and ones he also showed skill in. However, Batman has shown complete mastery over every single form of martial arts there is on the planet that is known to man. But, this is not just what gets Batman the win, he needs his gadgets as well. Captain America's greatest weapon is his shield. He has shown the ability to be able to throw the shield in such a way that no matter how many targets it bounces off, it will always return to him. However, this is given he is able to see the targets bounce his shield off of. If Batman uses a gadget to disorient the Captain, he has no way of getting his shield back. Then it will be easy for Batman to get close and put the fight directly to him.