I think that even though a carbine is "best on paper", the deciding factor should be personal preference based on experience, and the specific circumstances each person and/or home may have.
For me, I'm about 80% pistol, 20% carbine.
The 80% pistol is because it is likely what I will have closest me to if something were to happen, and I am not in my bedroom. I don't just open carry it on my belt when I'm in my apartment, but that is more so because I tend to not where pants when I'm home... But generally I always keep it within arms reach. If I'm watching TV in the my living room, it's on my side table next to me. If I go to the bathroom to take a shit, it comes with me. When I call it a night, it lives on my nightstand. If I think I hear something that I'm not sure may or may not be something, it's what I carry to take a look to settle my nerves.
More often than not, it is knocking at my door. You see, I'm the Resident Manager for my apartment building, and it isn't uncommon for me to get random knocks on the doors from residents who need something. Much easier to take a look with a pistol, than a carbine. If it is someone I know and trust, I have a high shelf directly next to my front door I can tuck it, and then help them solve their problem.
However, the 20% carbine is for when I KNOW something is wrong. If I hear something that I do not doubt for one second came from inside my apartment, or if something is literally trying to kick my door in.