Great matchup pitting Captain America against Batman. Although, the matchup that makes more sense is Iron man vs Batman considering they are both rich and have high tech suits that only their money could buy. If Hawkeye is battling Green Arrow and Flash is fighting Quicksilver, it would make more sense to pit Iron man against Batman. I think that would be too one sided though, Iron man would make short work of Batman.
It was mentioned that the fight between Bats and Cap would come down to who was more determined and I disagree. There was no mention of Captain America having superhuman strength. I'm pretty sure that Batman could not throw a motorcycle. Batman could use all the gadgets he wants, Cap is to smart and has a big ass shield. As good of a martial arts expert that Batman is, Captain America is highly trained. Captain America could take a punch from Batman, but not vise versa. It's likely that Cap could even hurt Batman even if punching his body armor. Batman would eventually get tired, Captain America could fight for hours and then go run a marathon.
It's clear cut to me that as badass as Batman is, he doesn't stand a chance against Captain America.