Play Twin Snakes and find out. Snake even defeated a more experienced Big Boss twice in a row.... as a rookie. Big Boss was even faster when he was old then he was when he was young. (You'll see if you play the original MG games...) And since he has been in lots and lots of wars, traning his CQC, gained much marksmanship (he joined a sniper range team and was a part of green berets and so on....) I'd put old Big Boss above Naked Snake, at least in some categorys....
Solid Snake also has alot of more impressive feats under his belt to...
Defeated the cyborg ninja, (Grey Fox) undoubtedly one of the most dangerous men in the whole MGS series, defeated Liquid Snake (same with him), even when Liquid was in a Hind-D (which he was ridicilousley good with) he lost against Snake.
Snake took down one of the best snipers of all time. (Naked Snake did the same, but it is not sure if he did it in a sniper duel or not. When he defeats the End he is holding his gun and his knife, the people on his codec advise him to get close to him, plus the fact that the End uses tranqualizers which makes it easier). Snake defeated her in a pure sniper battle, twice in a row....
Easily took down most people who came from behind, even some with stealth camoflauge. (Naked Snake got surrounded twice in MGS 3, and it seemed hopeless for him, but both times someone assisted him. This is kinda irrelevant, but it talks for his senses and his reflexes).
Snake actually dodged assault rifle fire, and even from a machinegun at point blank range.
I don't see what Big Boss has done to surpass that.... And that is only a minor part of what SS has done.