Honestly? WW Link? Like I stated earlier, WW/PH Link is so physically weak he gets dizzy from either the great spin attack or from rolling 3 times?! TP Link can roll throughout the entire massive TP Hyrule feild without batting an eye lid. Also, I completely disagree, if there is one Link that feels invincible, it is TP Link. He has so any different sword skills, and as someone mentioned earlier, his 'Mortal Draw' is practically un-blockable. WW Link to me felt fairly bog standard, his only advantage was that he knew when people would attack him and he could dodge, but I don't think any Link is as stupid as a Moblin and would simply watch him flip over their heads. Besides, while he'e flipping through the air *Bomb arrow* bye bye WW Link .
The 3-roll thing is from PH, which was technically an alternate universe dream thing, so I don't consider it much of an issue. The Hurricane Spin leaves him dizzy, but no other Links are actually flying around the islands at those kinds of speeds- would you be able to execute Hurricane Spin at all, much less do it without getting so exhausted you can't move at all?
Mortal Draw doesn't work on bosses, and again it leaves him vulnerable, so it's more of a situational thing, that like many of the Links' uber weapons would be unlikely to deal OHKOs or even do much more than a few hearts of damage. TP Link certainly has a myriad of Hidden Skills, but other than the jump strike none of them seem too useful in a melee. He's just not as agile as WW Link without the Back Slice and Helm Splitter, and his normal blows have a smaller arc.
WW Link is definitely not physically frail- his sword is plenty powerful enough to rip through the game's enemies, and again he's jumping and dealing consecutive 540 spin attacks even in his basic attack combos. He also wields the Skull Hammer and has Power Bracelets to shore up other physical weaknesses.
My main point is that WW Link is likely to do very well and come out ahead in the inital round of combat, which would likely see some of the weaker Links (OoT Adult, LttP, MC, OoX, maybe MM depending on masks) fall. His swordsmanship style is geared toward that type of melee, and because of this he'll likely come out of the first round with only a few scratches.
On the other hand, TP Link is amazingly powerful in duels, and could likely easily combat the other Links in single or even double combat. However, he'd have to be fighting very defensively to come out strong in the second round, since many of his skills (Ending Blow, Mortal Draw, Jump Strike) leave him vulnerable. As such, it all depends on his aggro in the first round. If he comes out battered by a reckless offensive, even with his skills he'll likely be too weak to take many more hits, making his riskier moves harder to use.
In short, it's really comes down to TP and WW Link, plus the few who survive the initial fight (likely Loz/AoL, MM, and Four Swords, depending on FS man count). TP Link would easily win the last moments, but his options would be really limited if he loses too much health early on. WW Link is agile enough to survive easily in the first round, so nutshell? TP wins if he comes out strong, WW wins if TP Link is too weak.
(BTW, Shadsie, what's the story with potions and fairies? What kind of healing can we assume here, and how should magic armors and such factor in?)
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(I'm just putting it in the master painting because I like it, not because I think it's much of a factor). I already voted, anyway. 
