BRD: dot crits reset an off-GCD ability, filler ability can force crit on your high-priority attack.
BLM: Fire can give free Fire III casts, Thunder ticks can give free Thunder (1/2/3) casts.
DRG: positional requirements to get the most out of its dps.
MNK: more positional requirements, and short-lived buffs that can fall off during dodge phases.

That's a bare-bones summary, kinda glossing over a lot. . .