Cap is superior physically all across the board, especially in terms of strength. Daredevil may have some pretty good durability and agility feats too (jumping off very high buildings without any harm, avoiding a room full of gun-wielding adversaries), but he doesn't have the strength to hurt Cap, and the shield will only tip the battle more in Cap's favour, especially with DD only being armed with a staff. They're probably about equal in terms of fighting skill though.
Nevertheless, I say Cap takes a solid majority in both scenarios.