Um, he didn't run off...we have no idea what in the world happens to Seifer after the fight with Adel except he's off with Fujin and Raijin at the end of the game. Where else is he supposed to go?

Oh and maybe Seifer could've fought her if he had two people helping him.

Squall was definitely portrayed as being stronger, at least towards the end of the game. During the beginning of the FMV, I'd say that they were on even terms with each other. Remember, Seifer might've given Squall a scar, but it isn't as though Squall didn't retalliate. Even after Seifer cheapshotted him with a Fire Spell (I'm assuming that they weren't permitted to use Magic in simple training bouts), Squall was able to give him a scar identical to his own. I'm guessing that's about where the fight ended, at least given that injury was sustained by both combatants. Yes, Seifer did probably have the upperhand seeing as how he had Squall kneeling, but he also had to resort to using Fire to do so. Taking into consideration the swordplay alone, the two appeared equally matched.

Either way, though, Squall definitely won their duel at the end of Disc 1, so it's really not worth arguing anyway. You simply can't deny that Seifer lost that fight. He even says something along the lines of "I...lost?!" or something like that. After the battle itself, he's on his knees with his weapon lowered whereas Squall is perfectly fine. At the end of Disc 1, Squall had definitely surpassed Seifer. Unless you want to try to argue that Seifer was holding back, but I really don't see how you could do that, considering Seifer was defending his beloved sorceress.

Yes, Squall did have help during his other fights against Seifer, but...what makes you so sure that he needed help? It isn't as though the party was tired after fighting Seifer. In fact, they had enough strength remaining after the fight to take on Edea, who was leagues above Seifer at the time. Yeah, Seifer did take out Odin, but I think that was more out of determination/adrenaline than anything else. Given the same circumstances (i.e. total desperation), I think Squall could've pulled off something like that during his initial adrenaline rush.

However, that's just speculation on my part. The fact remains, though, that Squall and Seifer only had one fair duel in which they were both going all-out, and Squall won. That's really all the evidence we have to go by at this point. We don't see either of them fighting in FMV's after that one duel, so we can't really say what either of them is capable of at the end of the game. All we have to go by is the training match (which basically ended in a draw), and the battle on the float (which Squall won).

I don't see this one at all. Seifer was just like he was at the start of every fight except he was more roughed up in this one. I don't see anything particularly different in his disposition or fighting except that he's gotten stronger and now has given up the Knight idea.

You have to remember, Seifer was basically a shell of a man by then. He'd lost everything; his pride, his dreams, his place at the Garden, even Fujin and Raijin had abandoned him. Though he might not have shown it, Seifer must've been a bubbling crackpot of emotion at that point. The guy had nothing left to fight for except for his romantic dream, and I'm willing to bet that he was prepared to fight tooth and nail for it. The sorceress was the only thing he had left. The fact that he was her knight was the only thing left to cling to, and now Squall and his friends were trying to take that away from him, as well. No doubt he was experiencing some sort of an adrenaline rush. Remember, actions speak volumes louder than words.