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Link (of TP) gets his Master Sword, Hylian Shield, and Hero's Bow (to compensate for his lack of throwing knives). Altair gets all four of his main weapons, and just for the sake of having something of a chance, their all his best weapons (as in the ones at the very beginning of the game that you ultimately regain near the end).

And for the record, Link does not get his wolf form for this tussle.

altair if he gets the element of surprise. otherwise i think link ends up taking it because he has a shield

as much as I love Altair link wins