Snake's Grenades, mines, and C4 are great things to batter Bowser with, but his main advantage is his overpowered tilts. They're much faster than Bowser's own, and even more powerful. Snake would rip Bowser to shreds.
Bowser does have one advantage, though; his F-air. He can gimp Snake with it's mostly horizontal knockback. A C4 here and there will make sure Snake doesn't die though, so it's not a very big advantage... miniscule, really.
In short, Snake against Bowser is probably 80-30 or so in Snake's favor. XD