I think it is too much work (aka, too hard to balance) if the limit breaks were all entirely different, as in had different effects.

I like the idea of how it is now, but I agree they should have different effects based on class.

Like...

Monk - Tifa's limit breaks (2, then 4, then all 7 punches)
Lancer - Jump, Juump (just kidding, hyper jump), JUUUUMMMMMP (lol, i mean dragon dive)
BLM - current ones are fine, skyshard -> meteor shower -> METEOR
Summoner - Because summoning primals/bahamut is probably storyline breaking, lets go with unused summons. Choco/Mog (teehee) -> Kjata (tetra element!) -> Alexander (judgement!)
White Mage - current ones fine, Healing Wind -> Breath of the Earth -> Great Gospel
Scholar - lets use summoning animations, clear tranquil (just the animation) -> Carbunkle (this fits pretty damn well) -> phoenix
Bard - songlike animations, healing wind -> pulse of life -> siren summon (but with the bard instead of siren).

Tanks -> no clue.