Shay for 2 reasons.
1. Better feats. Shay hunted hardened assassins. Connor hunted templars that weren't really fighters. The only true fighter Connor beat was Haytham, but only because Haytham hesitated. He had no intention of killing his son. Yes Connor tossed around the British army but Shay tossed around the French army.
2. Better equipment. Shay had a grenade launcher and two guns. Connor had a bow and a gun. Shay duel-weilded a sword and dagger. Connor had a tomahawk.
Also for those saying Connor is stronger than Shay, if he is stronger, it's not by much. Shay can stop a charging elk just just as well as Connor can. Don't believe me? Find an elk in AC Rogue then make it mad.
In the end Shay wins in a good fight.