A while back I made the switch from shotgun to AR after moving to the country. I've taken defensive classes for both and shoot both in 3Gun matches. My rationale:
Overarching criteria, any weapon I keep for HD has to be usable by my family members.
1. 5.56/.223 with suitable ammo does have less chance of over-penetration in normal dwellings.
2. I look at the AR15 as a system: I have my HD AR(s) and a .22LR and 9mm "trainers" that allow for cheaper practice.
3. AR15 has less recoil, so it's not as intimidating for newer shooters. My wife and son will not practice with a shotgun with OO. They will however practice with my ARs. I frequently have them both running plate racks with my .22LR and 9mm. Both guns are set up like my HD guns and function identically.
4. AR15 has inherently greater precision available, should the range increase, or should a greater accuracy requirement occur. I've practiced "scalloping" a TGT with a pattern edge, they haven't. Yes I could teach my wife/son "slug drills", but it's one more thing they'd have to practice.
5. AR15 has greater capacity, should not be an issue for HD with a purpose built shotgun, but there is a comfort of 30 rds of "point and click". Again, it's one less thing to have train/teach.
6. Living in the sticks, the HD AR15 is actually more likely to be used against a coyote than an intruder.