A turret firing slag bullets does 13% less damage per shot. This yields a 74% increase in DPS rather than the 100% that one might intuitively expect.
In Ultimate Vault Hunter Mode however, Slag elemental shots on Slagged Enemies receive 50% damage bonus, making the damage multiply by 258%.
A Double Up turret with Scorched Earth rocket pods does even less bullet damage, as the damage penalties for the two skills stack.
On the plus side, rockets fired from your turret deal double damage due to the targeted enemy being slagged.
Compared to Gemini, Double Up has slightly lower raw damage and does not effectively double turret health. However any slagged enemies will receive greater damage from both Scorched Earth and players, making it a stronger offensive choice.
However, Double Up has the side effect of not boosting turret damage on targets you or someone else slags. Normally, the twin guns make up for this but in Ultimate Vault Hunter Mode, where slag bonus damage is tripled, it becomes a disadvantage. This makes the slag bonus damage output heavily rely on player or teammate's gunfire. As a general rule, however, anyone entering UVHM will likely have extremely powerful weapons such as legendaries. This makes Double up a viable choice assuming one has good weaponry.
With the level cap increase, it is now possible to deploy 2 turrets with Gemini while retaining Double Up.