First by skill, personality etc...

Tifa vs. Zell
They both were trained and went thru massive adventures however Tifa tends to take things more seriously, while I wouldn't give this much precedence I don't see anything else to decide the fight.
Winner: Tifa!
Cait Sith vs. Quina
Rough, I liked both. Reeve however was a government man, this doesn't mean much for Cait Sith but whatever.
Winner: Cait Sith!
Red XIII vs. Kimahri
Kimahri worked as a guardian, Red XIII was the guardian of Cosmo Canyon before going on the adventure.
Winner: Red XIII
Sephiroth vs. Everyone
Silly question, Cloud's party beat Sephiroth and there not near everyone. However Sephiroth does blow up the sun... which then does 2000 to my characters.
Winner: Everyone
And by battle mechanics, though this is more according to which game the character is from. We will assume all stats have been maxed.
Tifa vs. Zell
The FFVIII system allowed 4X the speed, two hits from a 255 str Zell should be the fight, and if not he gets another before they both get the 4th turn around the same time. And if he limits -600,000 (assuming the controller isn't that goods -200,000) to Tifa's health bar.
Winner: Zell (1-1)
Cait Sith vs. Quina
Frog drop wins Quina the match easy, and KoTr wins it Easy for Cait Sith. Whoever's faster wins and I think the bar went up in FF7 faster.
Winner: Cait Sith (2-0)
Red XIII vs. Kimahri
A KoTr takes Kimahri and an attack takes out Red XIII, I don't know who the faster character would be. If Red gets the first turn he wins, if Kimahri does he quick hits, Red revives and battle goes until one runs out of MP, of course if Red had HP<-->MP switch this would last forever, Kimahri would run out first and it would be a toss up for the next turn. With how many tossups there would be...
Winner: Red XIII (2-0)
Sephiroth vs. Everyone
Winner: Everyone
Other Points: (not including X-2... because...)
FF8 characters battle sysstem has the ATB bar go up much faster than any other game, combined with hero, aura and limit breaks characters from this could easily defeat any other game.
FF7 characters have the continual revival which can only be beaten by the superior speed of FFVIII. KoTr is also enough to defeat anything.
FFX characters have crushing stats giving them 3rd place.
FF9 characters had 9999 attack for some + auto regen and auto revive.