I saw a short discussion of this fight the other day and I put almost as much time into thinking about it as I did reading that discussion. Writing about fights Cass would lose gets old, but I'm afraid Captain America would beat Cass.
Captain America can dodge machine gun bullets, for crying out loud. Cass can only fake that skill if she sees the person with the gun and reads his or her movements. That alone makes it unlikely Cass could tag Cap. Cass could dodge Captain America's shield because she'd know when and where he was about to throw it, but once they went hand-to-hand, Cap's greater speed, strength and stamina give him more than a slight edge.
More than likely, however, this fight would end shortly after it began because Cap would find a way to reason with Cass and convince her they're both on the same side and their little physical tete-a-tete is the result of one of those cliched comic book misunderstandings. Recognizing Cass as a fighter par excellence, Cap would impart some of his All-American leadership type wisdom then take Cass under his wing for a quick adventure, possibly breaking up some kind of Hydra-Intergang confederation. Then they'd go back to their respective comic book universes.
This would actually make a pretty neat story. I see it happening during Cass's Black Bat phase rather than her Batgirl days. Jim Steranko on art or at least Paul Gulacy doing his best Steranko impersonation.