I am torn between Skyward Sword Link and Ocarina of Time Link.
Sky!Link is definitely the most differentiated character as far as emotions and expression. This is largely due to the software allowing that kind of thing now, but it was also clearly a choice on the part of Nintendo. The "Link" to the games has always been a blank sort of character, with limited expression of his own, not just due to the software limitations of past games, but due to choice as the character is meant to be an almost-avatar for the player. Nintendo decided to make Sky!Link a little more of "his own" as far as characterization, clearly. It doesn't matter what you think of Zelda, Link makes the most anguished faces ever when she seals herself away. It doesn't matter what you think of an underwhelming treasure, he gets a crap-happy look on his face when he picks one up. It doesn't matter how industrious and caffineated you are when playing the game, you sit that boy down on a bench for more than a minute, and he's snoozing... Sky!Link definitely feels more like "his own" in regards to character than any of the other Links, and that makes him unique.
However, I also think the Hero of Time is unique, because, well... Way to go, Hero, you're the only one among your kind to BREAK YOUR UNIVERSE. I mean, his actions basically *broke Time* and created the split in the game-universe timelines. He also has the unique position and curse to sleep through half his childhood and to awake to being an adult, to live and fight as an adult and then to go back to being a child. Character-wise, I've always interpreted him as being a little messed-up because of that, confused as to his identity and so forth. A lot of the Links (including him, again, in MM) go through transformation experiences, but his transformation involved him jumping back and forth from unique life-positions. Then, of course, when he went back to his "own time" his heroism was presumably un-remembered. Living through another time and creating alternate universes with one's existence makes him unique. Again, none of the other Links BROKE TIME like he did.