Damage scales higher based on NP level regardless of how full the NP gauge is. For example, NP1 might be 600% damage while NP 2 is 750%. Even if the gauge is charged to 300% and goes last in an NP chain to bring it to overcharge 500%, the damage would still be the same
Overcharge only affects some or all secondary effects. DEF down debuffs, charm/death chance, etc... The higher the overcharge, he stronger the effect or the higher the chance of debuffing.