So first of all as far as Sniper vs. Gunslinger and 1 Gun vs. 2 Guns or 1 Shot vs. Multiple shots, don't let the animations confuse you. The animations are there to be pretty and are essentially just for show, under the hood the combat is still all dice rolls. That being said there is a slight difference, if you had 2 identically geared characters 1 being a Sniper and 1 being a Gunslinger you'd notice their base damages differ even though being identically geared.
A Sniper's base damage may read 1700-2000
While a Gunny may have Primary: 1350-1500; Secondary 350-500
So while technically yes a Gunslinger has both his primary and his secondary weapon dealing damage, it takes both the primary and offhand weapon to total the same damage as the single sniper rifle. Now, the offhand of the Gunslinger has a different accuracy, so yes there will be very marginal differences, but basically in practice the end result is that if both classes are identically geared, then Sniper=Gunslinger.
As to the argument that Gunslingers have 2 sources of damage so are less dependent on crits, again over a given period of time identically geared Snipers and Slingers will produce identical crit rates so it wont matter.
Now going specifically over the argument of Power vs. Crit after patch 2.0, its true that after initial testing most theory crafters were saying, 0 Crit All Power. As more and more practical parses come through though, it became evident that gearing really does depend on what spec or skill tree you choose. Using the Sniper/Slinger as an example, the Marksman/Sharpshooter tree does not have a lot of talents that boost Crit/Surge on certain abilities so those trees benefit more from a Power build, while the Engineering/Saboteur and Lethality/Dirty Fighting trees have a lot of talents with increased Surge and Crit percentages and so they actually parse higher when they sacrifice some Power for Crit in their gear. Keep in mind though that the differences rarely exceed more than 50 DPS and when you're talking about dealing 2650 DPS vs. 2600 DPS it isn't going to be a life or death outcome.
As to the question about lettered vs. unlettered mods there are a couple formulae you'll want to take into account. Basically every 1 point in Mainstat will give you +0.2 Bonus Damage and a very small amount of Crit%; and every 1 point in Power will give you +0.24 Bonus Damage.
So lets look at the unlettered Artful Mod 31
69 Cunning * 1.09 (+9% from skill tree) = 75.21 * .2 Bonus Damage = 15.042
57 Power * .24 Bonus Damage = 13.68
Total Bonus Damage = 28.722
Now the Artful Mod 31A
84 Cunning * 1.09 = 91.56 * .2 = 18.312
32 Power * .24 = 7.68
Total Bonus Damage = 25.992
So again, you're looking at a 2.73 DPS difference.... which is pretty insignificant so it isn't a huge issue if you only have one mod and not the other, but when given the choice, the unlettered mods are just that tiny bit better.
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