>>380
For the sake of consistency, I'll assume that every Link has all of the abilities from their game, but otherwise they're equal in terms of number of hearts, stamina, healing items, etc. Many of the Links have some sort of quick travel ability to get around Hyrule. Since the location isn't specified, and might not be Hyrule, I'll ignore this in general. Also, as a disclaimer, I haven't personally played most of these games so there may well be some details I've missed. Now, considering their combat capabilities in chronological order, and not counting remakes or games in the Zelda universe that do not feature Link:

• The Legend of Zelda: Unsurprisingly, one of the least well equipped of the Links. Has no advantage over any of the others and will definitely lose.
• Zelda II: The Adventure of Link: Actually pretty powerful. Has abilities that can shoot fireballs, reflect magic attacks back at their users, and summon lightning that kills enemies instantly. A strong contender.
• The Legend of Zelda (Board Game): No chance. Has no offensive powers besides a number of abstracted sword icons.
• Zelda (Game & Watch): Very limited abilities. Nothing that's going to swing things in his favour.
• The Legend of Zelda (Nelsonic game watch): Doesn't appear to have anything but his sword and boomerang. Not going to win.
• The Legend of Zelda: A Link to the Past: Another strong contender. Any of the three medallions can kill almost everything onscreen, plus he can escape into the Dark World with the magic mirror, and become temporarily invulnerable with the cane of Byrna, or invulnerable and invisible with the magic cape.
• Zelda no Densetsu: Kamigami no Triforce (Barcode Battler II): I couldn't find many details about this one, but I'm not hopeful about his prospects.
• The Legend of Zelda: Link's Awakening: Doesn't really seem to have access to any item/ability that others don't. Not likely to win.
• Link: The Faces of Evil: The book of Koridai is shown to instantly trap Ganon in its pages. Assuming this can be used against his fellow Links, he could consistently defeat one of them, but after that he doesn't have any game-winning moves up his sleeve.
• Zelda: The Wand of Gamelon: Link is captured for the entire game so his combat abilities aren't really shown. I'm going to go ahead and assume he'll lose.
• Zelda's Adventure: As above.
• The Legend of Zelda: Ocarina of Time: The titular ocarina can summon rain, change the time of day, summon a few NPCs, none of which seem amazingly helpful. Otherwise has no particular abilities that most other Links don't get.
• The Legend of Zelda: Majora's Mask: In addition to the above abilities, the ocarina can now transport Link backwards and forwards in time. Link can also transform with the aid of masks. The most combat-notable options are the blast mask (explode at will), stone mask (be overlooked by enemies), Goron mask (rolling attacks and access to powder kegs, more powerful explosives), Zora mask (swimming, boomerang attacks, and an electric shield), and the giant and fierce deity masks (augment combat abilities). Perhaps the most versatile of the Links.
• The Legend of Zelda: Oracle of Seasons: Can summon an animal companion with his flute, and the magic ring has a few abilities that could come in useful. Fairly average overall, not likely to come out on top.
• The Legend of Zelda: Oracle of Ages: Can travel through time with the harp of ages. Doesn't seem to have any other abilities that would confer much of an edge.
• The Legend of Zelda: Four Swords: Contains four separate Links. This would be a huge advantage if they can work together, but given the battle royale format, I'm assuming they are fighting one another as well as the other Links. They can only equip one item at a time and have no inventory, giving them a huge disadvantage over the others. Definitely not going to win.