*sigh* If you are faster in a battle your chances of winning is greatly increased. You can dodge the opponents attacks and land more of your own blows as well. Tifa is obviously faster than Aeris. (Have you ever tried to haul ass in a dress? It's a pain in the ass trust me, esp., if you're wearing high heels.)
Secondly, Aeris is not a offensive fighter. She is a defensive fighter, when she fights, and a 100th level cleric to boot. Her damage is very low and there's a reason why she is automatically put in the back row in the game.
Now, if you assume that both of them have maxed MP and HP, the situation is easier to look at. Let's do so from now on, it makes things so much easier. Now, if Aeris can use materia, then Tifa can as well. Aeris uses GG and attacks Tifa, Tifa can simply use Regen, Big Guard, and then stop on Aeris to counteract Aeris' attack, until GG wears off. Then it's time for an asswhoopin'. I'm sorry, deny it all you want, but Tifa will win. At least she survived in the game.