Link is clearly the reigning hero champion. Not only in what he does, but what he fights. The Bosses and Minions of the Zelda series are clearly monstrous entities, where Mario fights... mushrooms, toon-ghosts, and turtles.
Although, I might have had a tougher job determining whether Luigi or Link were a bigger hero. Luigi fights the same monsters as Mario, but he's not fighting for the love of a lady - he's fighting for his brother, and because it's the right thing to do (even if he's rather frightened of the prospect of being a hero).