Snake would absolutely beat the shit out of Master Chief if we were comparing MC from the game series.
Fuck the books, MC cant do any of that shit in the game.
In the game he moves fucking slow, cant do no hand to hand combat shit, cant lift shit all and seems like an amazingly crappy generic character. He just looks like an ordinary futuristic soldier in the game, but in the books he is ridiculously powerful, so things obviously do not match up.
Compared to Snake or rather the MGS story as a whole, Snakes abilities are consistent through out, unlike MC where he is crap in the game but amazingly good at killing people in the books. This is why i do not rate MC at all because he has no personality what so ever and has never shown any real determination or anything of that sort in the games at least, compared to Snake who has been through a fuking microwave filled corridor whilst being half dead at the age of like 50/60 or however fuking old he is.
To sum up,
MC (from the games) vs Snake = Snake would beat the shit out of him
MC (from the books) vs Snake = almost certainly MC would win