Cid and Red XIII's weapons are based on MP, as far as I know. Barret's is based on the amount of AP in the materia junctioned in the weapon. Yuffie's is based on the opponents level, Cait Sith is mostly like Cloud's, I think, though I never used it.
I think Yuffie's is the best, because it deals the same damage when morphing, while all other weapons deal 12.5% of their max (unlimited*) damage, or something like that. She should be doing 9999 at level 50-60 or so against northern crater enemies.

*By unlimited I mean the damage it would have dealt if the limit wasn't 9999.