If you are only permitted one, I think the fundamental question should be this: Which scenario is more likely in the first place, a single home intruder or an attacking mob?
That should settle the issue.
AR in your arms and a KSG slung in a pouch on your back. .45 in a shoulder holster and a tack vest full of mags.
Or a DP-12. In an invasion scenario I’d want a belt fed weapon.