Way too many factors involved without some clarification.
Here, most of the homes are concrete block and some of the older ones have block interior walls, pretty safe until you get up to to around 30-06. In your typical stick built home the parameters change a lot.
A shotgun load is carrying at least a 1 oz. load of lead that hangs together for 25-50 ft., well over the average 'confrontation range' of 8-12 ft. in most home invasion situations. It's also unwieldly unless you have a large home.
My choice is a 13 rd. 9mm. with snakeshot as the 2 first rds. This easiliy allows for 'first stike' capability without penetrating walls. Sound, muzzle flash and pain/possible blindness should subdue most intruders. If not, 11 Black Talons and a back-up mag of Hydra-Shok's should solve the problem or buy me time to get to the Mini-14. Not that any one would really consider a full on assault on MY house, not a whole lot here unless you like women's clothes.
