Shelley Rae has an interesting write-up of pistol carbines as home defense guns.
I must say its an option that is often chided by people who might chose a more effective or convenient gun. I like Pistols for HD just because they’re maneuverable and you can keep them hidden, like say answering the door to an unknown, but non-threatening caller, without any awkward explanation to the neighbor looking to borrow an egg on why you have a long-arm slung.
Some prefer shotguns for their amazing close-range stopping power. There’s a lot to be said about something that can deliver that much lead on target quickly.
others prefer carbines, often in 5.56x45mm for its ballistics, and certainly with the correct ammo less risk of overpenetration than you might think.
Still I must say pistol carbines have a certain thing going for them. Most of them eat from ample magazines, and many of the new ones on the market share magazines with common pistols (which is AWESOME if your pistol will eat from the same hopper as your carbine), they have extremely low recoil, and all the inherent accuracy of a long-gun. Certainly I wouldn’t recommend a shotgun to a recoil sensitive person, and I know people where even a 5.56×45 gives them a bit more boot than they prefer. Meanwhile a pistol carbine will kick less from a lighter package. Also an interesting side note, if you shoot sub-sonic ammo, they’re also quite quiet. You still really should wear ears on the firing line, but in the close confines of your home you’ll have that added benefit of shooting a suppressed pistol or carbine, which when you look at the reality of permanent hearing damage of say touching off a rifle or shotgun inside, that’s a monster plus.
The only thing you really lose is maneuverability of a handgun (tho technically you gain a bit of muzzle energy from that same pistol ammo, tho the end result is mostly academic) and the stopping power of a rifle or a shotgun. But if you say have a Sub-2000 eating from say a 33 round Glock 18 Magazine you can make up for this with quick follow-ups.
Certainly something to consider.

