Round one sudden encounter no prep, morals on Round two 30 minute prep, morals off Bonus encounter. Bucky team up with Cap, Winter soldier gear, round two applications, the dc character can team up with someone, as long as its a close battle.
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I would take Cap over most of the street-level leaguers (Green Arrow, Black Canary, Batman, etc.) and any two man team along with Bucky. A lot of those would be close, esp any fight against Batman, but like I said I could see Cap winning for sure. He could probably beat someone like Star Girl too, whose only power is flight/projectiles. I'll go ahead and say anyone without powers, except Midnighter (does he have powers, doesn't he? I dunno in the new-52) in DC and is not a suped up tech machine (ie Cyborg) could be beaten by Cap. Most people in DC w/ powers would probably beat cap tho, given how OP most of them are. But to put a single answer to your question: Bane.
@Calildur: I understand, my answer remains the same. I don't think his healing factor is good enough to stay toe-to-toe with most of the legit super-powered folks in DC. They are simply written to be more OP than your everyday superpowered ppl in Marvel. For example, Beast Boy isn't exactly a DC powerhouse and would get trounced by the upper-leaguers, but I don't see Cap doing squat to him. Cap is a hell of a h2h fighter, and the ultimate version is even tougher, but in a battle like this that's all he really brings to the table. Without a team of other people w/ more versatile powers to bring to the table, his tactical genius just doesn't go far enough against the kind of superpowers you see in DC. But like I said, he could take down pretty much every street leveler except Midnighter (who really isnt even a street leveler any more) in DC, which is damn good IMO considering that includes people like Batman and Green Arrow.