Bennett,
My opinion only (moo). Shotguns are your best choice. If you dont have a home defense shotgun, but you have an AR, well fine. If you can get a shotgun, shoot some prairie dogs with the AR.
I know that previously I have mentioned an 870 Marine Grade as my favourite and to a certain extent it is. However, oberkommando mentions his M1 Super 90. I believe Benelli to be the best make of shotgun in the world. I have always hunted with Benelli's and own two 121SL80's (pre Rafaello, Montefeltro, Black Eagle, super 90, etc.). At least 10 of my shooting buddies own the M1, I have shot them and know of nothing better. One guy has a mag extension that allows 9 in and one up the spout. Loaded with anything from #1 buck to 000 buck, this will stop all ten intruders and possibly a few more if you catch them in a corridor and can hit the first guy or two in the throat as some of the pellets should pass through and get a guy behind (just a joke).
Seriously, dz is one hundred percent correct. Think about possible HD threats and what can neutralize them. If you need all 30 in an AR magazine, you better hope the neighbours wake up and call the police 'cause you need help!
The point is, shotguns properly loaded and handled are more than adequate for home defense. Friends, very seldom will there be an engagement range exceeding 7 or 8 yards in the average house or apartment. The most important thing is shot placement. Your first shot must count.
Just a thought regarding the issue of overpenetration of high powered rifle cartridges. I define this as shooting someone that you didn't want to shoot with the bullet passing through walls and things like that.
There, is another problem which is potentially more catastrophic. This is riccochet, which I define as unintentionally shooting yourself.
In a home defense situation, I believe most of you would agree that it would be a catastrophe to be shot by a bullet, fired by yours truly, reflecting off your decorative brickwork mantelpiece.
Suffice it to say that I am not a big fan of either possibility. The Franchi spas 15 was developed as a paramilitary weapon for house to house work, room clearance, etc. to reduce or eliminate the possibility of friendly fire accidents in close quarters. It is a shotgun that you could mistake for an AR carbine on a dark night. The point here is that overpenetration and riccochet are big enough concerns that a Manufacturer decided to build a weapon with the perceived benefits of a modern assault rifle and it happens to be a shotgun.
Remember MOO.
ENJOY SHOTGUNNING and try ISSF Skeet.