What kind of a shotgun? Sounds like a hell of a trade! From what I have read it seems that the .380 is a decent defense round. There are better out there, but you will be giving up some concealability. I would have no problems carry a .380 as long as it shot accurately. If you can hit what you aim at then I would say you are good to go. The .380 can penetrate enough to be good defensively.
Check out "the box"
From the tests he did, the .380 HP round penetrated 4 1 gallon jugs and expanded somewhat (equal to 12" of ballistic gelatin.) The .380 ball round penetrated 5 jugs.