The most effective rounds in a shotgun are #1 buck and larger. Using birdshot - even inside the home - isn't recommended. If you think they'll stop in sheetrock and walls, try it - doesn't work. What it doe wrong is that it doesn't penetrate enough. A dude caught a load of birdshot in the chest, inside a house, and was sitting on the curb waiting when the ambulance arrived. The wound looked horrible, but was almost entirely superficial.
Instant incapacitation? Hardly. The reason the guy stopped was because he didn't want to be shot again - if he'd been more motivated, he could have finished the job.
Personally, I won't take that risk.
And yes, buckshot goes through walls too, just like pistols and rifles.
While I always carry a pistol, it's the next to last thing I want in my hands if I need to shoot someone. If you feel a shotgun isn't appropriate for your purpose, look into a carbine with the Hornady TAP round. Like Mickey said.