That was a well thought out, good argument with many reasons behind deep and meaningful statements xtreme112.

My Analysis goes:
Squall has better training, he was trained to be an elite while Cloud was a grunt soldier. Cloud was boosted by Mako powers (which we can't evaluate) while we know Squall is hugely boosted by GFs. I'll call this even though battle system evidence leads us to believe Squall gets a greater boost. Cloud's FMV achievements are definitely more impressive though. I'd say they both have advantages and are different fighters though I would give Squall an edge.
In-battle:
Squall at 170 speed is about 4x as fast as Cloud at 255. So in his 4 turns he could easily toss himself a hero and cast aura before absolutely destroying. And if it didn't kill Cloud he's in invincible with 4 turns to Cloud's one.
Actually:
a) There in different worlds.
b) Squall fights for a purpose (though it may be as simple as work), I think by the end of the game thiough he wouldn't fight for something he didn't believe in, and as there would be no point in him fighting Cloud I don't think he would.
c) Cloud's easier to see fighting the other as a mercenary but he also develops throughout the game making it again unlikely that they'd fight.
d) So no, they probably wouldn't fight.
e) Your mom.
f) On the other hand there is not much of a chance they'd fight each other alone:
As shown above the battle system hugely favors FFVIII characters.
FFVIII characters also have consistently far more training. The FFVIII characters had the most training in the storyline of any of the later FF (possibly all but I'm not an authority) so they'd be favored in any match. The speed in the battle system also makes them the strongest in a direct comparison so that can be considered accurate.

Winner: No one, or Squall