Freya gets a Coral Ring if she wins, and that will help teach some abilities, and Lancer, one of Freya's ablities to decrease HP and MP. IMO it's as strong as Jump but without the extra delay.

Zidane wins 5000 gil, and consider the fact that the Coral Ring takes about 1000 less gil to synthesize (believe me, I calculated it), you'd get more bang for your buck if Zidane wins.

Vivi wins a card. Absolutely worthless since you can get the card later in the game.