I'm assuming we're being realistic about all this, so "TP Link only takes a quarter heart of damage!" and that sort of thing doesn't apply. I'm also assuming they're at maximum power and have basically reached the ends of their games.
Who Would Win
OoT/MM or TP Link. OoT Link has a plethora of spells and isn't too shabby with a blade, although he never appeared to be trained like the more recent Links were. MM Link would theoretically have a bunch of masks with him. Fierce Deity Link would wipe the floor with anyone, but even without that ability, try fighting someone you can't see (the Stone Mask) or who runs at superhuman speeds (the Bunny Hood). OoT Link has the Triforce of Courage to bail him out as well. TP Link, meanwhile, is a trained fighter who also has the Triforce of Courage, and his constant acquiring of Hidden Skills throughout the game (by a post mortem OoT Link, no less) makes him even more formidable. He doesn't have any magic, but his deadlier arsenal of a bow, massive ball and chain, two Clawshots, and possibly Magic Armor should offset that imbalance.
Who Would Lose
The Link from the first couple of Zelda games; possibly the Links from the ALttP/LA/OoX games or Four Swords. The only notable thing about Four Swords Link is that there are four of him. Take that away, and he's the simplest of the heroes. I've only played Link from Link's Awakening in that game, so I'm not sure how powerful he is in the other games, but he also seems a bit of a simplistic hero in LA. The original Link, again, isn't that noteworthy, doesn't know magic until the sequel, and has a very basic arsenal. We don't know if he's a trained fighter or not, though he can probably survive in the wild considering he's implied to have been a wanderer before Impa bumped into him.
Despite my previous statement, we've got to give it up for Link's portrayal in Zelda II, right? He goes all the way through what's said to be the hardest game in the series, surviving onslaughts of powerful enemies, only to have to kill what's essentially his clone at the end. Perhaps his magic wasn't as potent as that of other Links, and perhaps he too was simple. But you've got to give him credit for reaching the end of the game. Tough cookie, right there.