Does a slag weapon deal more damage?

Bullets from elemental guns do "bullet elemental damage", which is different from "elemental damage over time" a.k.a "status effect". Slag bullets are not amplified by slag status effect.

Slag does not inflict DoT or do bonus damage, but it will deal 100% damage to any target, while Corrosion is penalized against non-Armored targets:

• In Normal difficulty, corrosion will do 90% damage to flesh targets, and 75% to shields. Factoring in corrosive DoT, the damage is somewhat equal. Corrosive is obviously better for Armored targets.
• In True Vault Hunter Mode, corrosion will do only 60% and 40% to flesh and shields, so a Slag weapon becomes much more dependable.

See wiki for a table of element effectiveness.