sure:
Level 2 PC 16 Dex, Two Weapon Fighting Style, 4 rounds of combat vs AC 14. Starting combat with a normal (non advantage) attack.
Average total damage over 4 rounds:
Two pistols with Vex: 40.7 (assumes short range)
Two shortswords with Vex: 30.8
One Shortsword and One Scimitar with Vex/Nick: 28.3
These numbers include advantage from vex, crits and it includes increased chance to crit from Vex when applicable.
Wow, that took me like three times reading it to understand what the heck you were doing. But, there are a LOT of assumptions that need to be noted.
For example, you are assuming that you are within 30 ft, but never in melee with the enemy. As a dex based character you are often going to be going BEFORE the enemy. So, that means you need to move within 30 ft of the enemy, still have movement to retreat from the enemy, and the enemy cannot take the dash action. Because if they do... oops, disadvantage on those pistol attacks.
But, breaking down this math....
16 dex, +2 prof, looking at a +5 to hit. AC 14 means you hit on a 9 or better. That is the standard 60% chance to hit.
Damage is 1d10+3 or 8.5. First attack would be 8.5(0.60)+5.5(0.05) or 5.375.
Second attack has a 60% chance of having advantage. So, if I have this correct that is 0.60(8.5(0.84) + 5.5(0.0975)) + 0.40(8.5(0.60)+5.5(0.05)) or 4.606+2.15 = 6.756
And it gets more complex from there, but I'm fine saying that this looks like about 12.13 per round
No, what does the Shortsword and Scimitar do? Well, using that same math
Damage is 1d6+3 or 6.5. First attack would be with the Nick weapon for 6.5(0.60)+3.5(0.05) or 4.075
Second attack is the same 6.5(0.60)+3.5(0.05) or 4.075
Start of next round has Vex and is 0.60(6.5(0.84) + 3.5(0.0975)) + 0.40(6.5(0.60)+3.5(0.05)) = 3.481+1.63 or 5.111
So, first round is 8.15 with the next round being 9.186 on a good day. However, no need to worry about the enemy getting into melee, and if the enemy avoids melee then you can just pull pistols.
But where this gets interesting is with Hunter's Mark. Because Hunter's Mark hurts your damage for Pistols and helps your damage for Shortsword and scimitar.
Cast Hunter's Mark for the pistol, then you drop to just doing 12(0.6)+9(.05) = 7.65 on that turn, dealing 15.3 on later turns unless you have to switch the mark.
Cast it on the Scimitar and Shortsword, and you get this
10(0.60)+7(0.05) = 6.35
10(0.60)+7(0.05) = 6.35
And that ALONE is 12.7 which is BETTER than what I calculated for your dual pistols without Hunter's Mark. And, by looking at my math, I likely ended up with higher numbers than you did for the pistol.
And on later turns you can get
0.60(10(0.84) + 7(0.0975)) + 0.40(10(0.60)+7(0.05)) = 5.45+2.54 = 7.99 + 6.35= 14.34 per turn
So... it only sort of works. Yes, the Pistols can be more damage, if you have nothing to spend the bonus action on and if you can keep at the proper range. Of course, you can take a feat to remove that range restriction... while the dual-melee build is spending feats on improving their damage or increasing their defenses. So I don't think this is as cut and dry as you made it sound.