There's a lot of unconfirmed theories as to how Two Shot works...

One theory I read was that the max damage of each shot is effectively reduced to 80% of max damage. If both shots hit, then the weapon does a total of 160%, but if one shot misses (shooting at a fast moving target), then the weapon only does 80% of it supposed max single shot damage.

IMO it is the Overseer's Rifle from Vault 81 modded to shoot 308 and large mag. You have 40 rounds of semi-auto 308 doing double base dmg. It has very good DPS.

This ^^

With a .308 receiver on it and maxed out Rifleman perk I'm one-shotting super mutant butchers from a hundred yards away, playing on very hard. And I haven't even started in on the perks that give sneak attack multipliers yet.

Overseer's Guardian is great - especially because you can get it really early. But I much prefer it as an unscoped, medium range gun.

With the appropriate perks, the Instigating Gauss can get over 2400 points of damage in a single shot from surprise. That's like five or six mini-nukes, and is so OP that I don't think there is anything in the game that comes close to having that many hit points. Maybe a Survival Mirelurk Queen? (What's the hit point multiplier for Survival, anyway?)

Wouldn't a Legendary Gauss Rifle with the two shot prefix be far superior, though? Assuming of course it's possible to find one.

Yes. I had Overseer's as my sniper rifle at first but converted it back to a normal unscoped rifle after. It's just a beast for medium range encounters.

I dunno, I have a bunch. Mostly it's the +50% Damage to Super Mutant fully modded .50 Sniper I built from the .308 Legendary. I use Old Faithful sometimes, robots hate it, which I built into a fully modded Laser Sniper. The Gauss I leave at home mostly, although it hits really hard. It's heavy and my load is too much anyway. I have the Railway Rifle as snipish as I can get it but it's heavy too.

My mid range guns do most of the work anyway. My stroked Assault Rifle, Baby, my tricked out Plasma Rifle and my .308 Combat Rifle I made are just golden.

This is what I did, it's extremely powerful! It one hit body shots 90% of humans and ghouls. I have a reflex sight on it so I can't snipe as well. But as a sniper it would be amazing I'm sure.

THIS !

Some say it's Overseer's Guardian, some say 6 crank laser, some say .50 cal fully modded sniper.

I can say Gauss has the highest damage and I tested all of the above. Best if it has a legendary prefix like 'instigating' (double damage if target is at full hp) or 'shoots an additional projectile' (though the second projectile doesn't seem to benefit from damage perks) then you can pretty much 1 shoot almost everything in the game from sneak at survival difficulty. Considering that, I would choose Instigating as it is practically double damage.

Of course it's nice to have rifleman, lone wanderer, bloody mess for damage and ninja + sandman + Deacon's perk for sneak damage multiplier, for up to 6.3X. And Gun nut and Science to mod the hell out of the gun. Sneak perk helping a lot to remain undetected to get that imba multiplier.

The Gauss named 'The last minute' is easy to get/buy and doesn't need hours of legendary farming like the instigating or additional projectile, and it still does 552 damage with the perks above, and you can put a suppressor on it, making it benefit from Sandman.

So total damage: 552 x 6.3 = 3478. Even a trip to the Glowing Sea will seem easy with this kind of damage.

Getting ammo for it is also easy, but I'm gonna stop here with the spoilers.

Yep. The overseer & the Gauss rifle..never leave home without them..and if couse some grenades and bottlemines..., that's all you need....

Tbh I actually think the Gauss Rifle acts more like a energy weapon shotgun. That's what I've been using it as xD