Tifa, game play wise, was fairly poor. She was very good at first (but that is not difficult given how little characters you have then). Many of her knuckle weapons dealt fairly average damage. While her final two weapons are very very good, with Godhand having 255% accuracy and Premium Heart dealing more damage the more her limit break filled.

In fact, keeping her limit bar filled is a decent idea, because her reels are fairly tricky to pull off successfully, and only get harder as you earn more reel slots.

Meanwhile Red XIII is well rounded with both physical and magical capability, and has the second highest dexterity. His ultimate weapon isn't hampered by having a full limit bar (meaning you can't actually attack normally). His limit breaks are split fairly evenly between buffing and damage.

I have to say Red XIII. Game-play wise, he is just superior to Tifa. I didn't use Tifa that often really in many of my playthroughs of the game. While Red XIII isn't the best character in the game, he is definitely up there. Plus his characterization is just fantastic.