Most of the characters are statistically almost the same, but as mentioned there are some minor differences, and the some of the characters actually have classes, even though they're not really utilized that much. E.g. Yuffie is a thief, Tifa is a monk, Cloud is a warrior, Cid is a dragoon and Aerith is a mage.

But yeah, Aerith can be used as a mage more so than the others since her magic is stronger, her attacks are weaker and her limit breaks all have a healing effect.
Also, you can put Long Range on characters like Barrett and Vincent since they have guns - other than that I can't really remember other significant stuff.
As others have said, it's not so much about the stats in this game, but then again I guess it depends on how you decide to play the game.