Piercing works out to a 14% damage bonus on enemies with more that 50% of your weapon's damage bonus, and is always inferior to mighty.
On weapons with high damage scaling bonuses work best
Two shot* > Mighty > violent > piercing
for low damage weapons with a high rate of fire fixed bonus damage work best
Bleeding > explosive* > freezing > energized = plasma infused > poison > burning
notes
Two shots adds the weapon's base damage, then deals half the listed damage with each shot, meaning a weapon with highly upgraded damage does not benefit as much as a weapon with no damage upgrades, while weapon's whose damage is reduced by upgrades benefits even more. A full upgraded 2 shot gauss rifle gets less than a 50% damage bonus, while a fat man with the mirv upgrade receives a 200% bonus
explosives deal more damage on heavy weapons like the minigun, because the heavy gunner perk and explosives expert both apply, and increase the damage of the explosive to 60 damage per shot, the other effects only receive one damage bonus, meaning bleeding only reaches 50
Burning and poison don't stack with themselves (bleeding does), meaning unless you are only shooting each enemy once every 5 seconds you are wasting the bonus damage with every shot, and poison is better than burning because poison resistance is far more rare than energy resistance.
freezing is better than energy and plasma damage because it freezes on critical hits in addition to the normal damage bonus.