I think it depends on how you consider using it. IF you plan to gather your family and hole up in a safe room, etc., and either deal with intruder who comes in, or police arrive to investigage, a shotgun is fine. I"m not too keen on the pistol grip (oply) versions, to me the shotgun is best shot from the shoulder. At house ranges, pattern is narrow, easy to miss if not aimed.
IF you plan to be armed when say a knock on door at strange hour, you need to go outside to check out something unusual, wife, etc, plans to train with it, then I think a good revolver is best, short barre., easy to conceal, etc. If wife is to be trained, the manual of arms for a pump shotgun is somewhat complicated, ie, safety, action release, unload a chambered round, etc. etc.
Even in daytime, say a knock on door, really are you ( or anyone else ) going to go to the door with a shotgun, to great the UPS, USPS, Jahova's Witness, neighbor wanting to borrow an egg, girlscout selling cookies, etc. etc. etc. A snubbie works just fine for that. BUT, for a S.H.T.F., when you are making a stand, inside a room, it's hard to beat a shotgun, use small shot, BB, etc.
Mark