When I first started to wander the wastes in search for weaker enemies to make some XP, I had a 10mm pistol and a (basic) shotgun. The reason: I wanted to use the pistol most of the time, but switch to shotgun if one of those raiders managed to get near.
The point is, I don't know if this happened to you, but my shotgun tended to do the same amount of damage than my 10mm pistol. And what is worse, burst mode seemed to do the same amount of damage than single mode most of the time. One could say that I should not complain about this, since both the 10mm and the shotgun can be crafted by a noob with no profession. But I was expecting to get something in change for just being able to load TWO freaking bullets in a shotgun. In other words, shotgun worked simply like a 10mm pistol with a two bullets magazine. Conclusion: shotgun was useless.
I think the shotgun needs to be more than this. One should need to care to avoid getting close to an enemy who's wielding one, even if its a basic one. I wouldn't be amused if some sucker shot me in the groin with his shotgun.