The answer is a resounding yes. Bane may be super strong due to his Venom, but Cap has fought stronger. If he can deal with a rampaging Hulk, than Bane is cake. Not to mention, that Captain America is a way better fighter on his feet.
WINNER: Captain America
And I would go as far to say that Captain America would have never been defeated by Bane during the Knightfall story line. Obviously, Batman could defeat Bane. The villain’s only chance to win was his master plan of distracting him to exploit his vulnerability: Batman’s pride.
Batman didn’t ask for help and almost lost his life–and the city as a result. But Captain America is everyone’s favorite super hero for a reason and would have decided to call in favors for the betterment of everyone.