Hmmmmm. I'm a bit of a fanboy of both of these characters...
I'ma go with DD on this one. Cap's shield is worthless. DD can sense exactly where the thing is going with his radar sense no matter how many times the thing rebounds off of walls and the floor. And considering that pic posted of DD whacking Cap with his own shield, I'm pretty sure Cap would remember that and just drop the thing and go toe-to-toe with DD.
I believe Cap is slightly stronger and faster and more agile than DD. I mean, he does have the utmost peak of human abilities in all those areas. DD is a regular human, highly trained and extremely close to peak human, but not more. I think he looks more agile because he can react to things faster on a mental and instinctual level than other people because of his radar sense. Either way, Cap's small physical advantage is essentially negated by DD's radar sense.
Who's the better fighter? Hmmm. Marvel's rating system is garbage. DD is clearly a 7 like Cap. I just happen to think that they'd both get a couple of shots in, but DD would take advantage of pressure points and his radar sense to end the fight.