As I have written before I am not a big fan of shotguns. A long time ago on the tactics list there was the famous "AR vs. Shotgun" debate which to my mind really put a lot of things into perspective. Your home defense gun should be a rifle.

Whatever you want to call the capacity for wounding - stopping power, knock down power, etc. Rifles have an order of magnitude more of it than handguns. Handguns are capable of poking piddling little holes, while rifles are capable of relocating muscle, bone, and large size chunks of vital organs to the area surrounding the assailant. I don't believe in one-shot stops, but having a weapon capable of relocating fist size pieces of brain matter is probably like to solve the problem with a lower round count. There is no comparison between rifle ballistics and handgun ballistics. When it comes to protecting yourself and your loved ones it would be foolish to opt for less effective weapon system.

The accuracy of handguns is perfectly adequate for the distances involved in a self-defense situation at home, but getting good accurate hits across a room is not a trivial exercise, especially against moving target that might be shooting back. The experts among you who can make 100m pistol shots, but the novices among you can make 100m rifle shots. Translating that to even shorter distances is much easier to small targets with a rifle at close range than it is to shoot the same targets with a handgun.

The AR (or AK) weapon systems produce minimal recoil, making accurate follow up shots quick and highly accurate even for people of smaller stature and limited training. Double taps, controlled pairs, or whatever your preferred plan of fire is will be much easier to execute.

The ammunition capacity, double that of even high capacity handguns, should be sufficient for numerous assailants. I have a hard time thinking of a realistic scenario where a magazine change would necessary for anything other than a malfunction.

The lightweight (especially in comparison to shotguns) makes these rifles much easier to operate and manipulate for people who are of smaller stature. An athletic 5' tall woman who would be challenged to operate a Remington 870 would have no problems with a AR especially in a carbine variant.

There are claims that handguns are more maneuverable, but this is a of a false comparison. A handgun at the locked out isosceles position is roughly the same length as a shouldered rifle or carbine. While there are edge cases where it might be hard to manage a long gun, most them are pretty contrived and can be solved with a better application of tactics and movement.

The conventional wisdom of the near-magical deterrent value of the racking sound of a 12 gauge is prone to some major flaws, the greatest being that the assailant has to be close enough to hear the sound. I would much prefer that the first sound the intruder hears be something more along the lines of "INTRUDER, THE POLICE HAVE BEEN CALLED! GET OUT OF MY HOUSE NOW! IF YOU COME ANY CLOSER I WILL SHOOT YOUR BRAIN OUT!"