Physically, they are pretty equal with DD being slightly faster & more agile and Cap being a tad bit stronger and he's got more endurance.
Skill-wise, like it or not, DD is a better more well rounded conventional fighter mixed in with not-so-conventional exotic mystical combat training that, again, like-it-or-not, Cap won't know how to deal with.
That shield won't ever, ever, ever, ever hit DD. It won't happen, it can't happen...DD will know where it's at at all times. He'll have a better idea about where it'll be next than Cap himself will.
The fight would go on for a while seeing Cap throwing, and continually missing DD with his shield. It honestly wouldn't surprise me if the shield ended up in DD's hands.
If it does, DD murders Cap. If Cap plays smart and decides not to use the shield for anything but defense, it's a stalemate.