Its because of the Potency of the Limit Break as well (which affects the damage the same way as normal attacks, but uses the parties damage rather than the individuals damage)

Caster: 1400/3000/5400 (AoE)

Melee: 2300/5000/9000

So when an LB is used (especially on a boss), the Melee LB will do a lot more damage than the Caster's LB would.