Anyone thinking "fighting dirty" gives Batman some kind of advantage is pretty much completely ignoring that Captain America fights people that "fight dirty" all the time. The difference being those people are usually trying to kill him, and Batman absolutely will not.
Cap has superior physical attributes, virtually unlimited endurance, and experience in his favor.
The only way Batman could take the win is if it takes place in Gotham at night. Batman would have to use superior knowledge of the terrain and push his stealth to the maximum to have a chance. He'll also have to end the fight quickly, as noted above...the longer it goes, the more it falls in Cap's favor due to superior endurance.
Pretty much anywhere else? Cap takes it. Not easily, and not without plenty of cuts and bruises himself, but he takes it.