If you ever find a double-barrel with the no-reload mod, that's your weapon for the entire game. It's only limited by the reload time, so if you do, it's basically a super high damage autoshotgun that also does absurd crit damage.
Are double barrel higher damage than combutt shotguns?
Massively. It's got 5 lower base damage unmodded. However, the effective DPS if both are bottomless is much higher even when both are unmodded-the double barrel has a base fire rate of 36, while the combat shotgun has 20 (30 with the Rapid automatic receiver),
and the double barrel has both higher base damage and higher RoF when fully modded (and you can fully mod one very early on, it only takes Gun Nut 2).
A fully modded double barrel has 96 base damage and 181 base RoF. A fully modded combat shotgun (semi-auto actually has better RoF than auto unless you want to entirely forgo bonus damage and get Rapid) has 106 base damage and 26 base RoF. Moreover, the best barrel mod for the combat shotgun reduces recoil and spread, while the best one for the double barrel (sawed off) is (IIRC) doubled crit damage.
You can get one set up early, and with a crit-oriented build + Rifleman that double-barrel can oneshot almost anything in the game. If you don't have to worry about reloading, it can also fire far faster than the combat shotgun. But even without that I still prefer the double barrel simply because all you have to do is charge a crit, sprint up, and unload on something's face. Instant dead.
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But yeah, the explosive bullets legendary is great on shotguns because each pellet explodes.