The AK/AR is best for home defense because naturally your going to hit the target more frequently, it's not as long as a legal shotgun, has 30 rounds, rarely jams, plus its imtimidating.
There really isn't a rule that states that a semi auto rifle will hit a target more frequently than a single shot 12 gauge. The 30 rounds doesn't hurt though. But when you unleash rounds you have a responsibilty to your family members and your neighbors.
Personally, if someone broke into my house I would attempt to identify with voice, naturally if they don't answer I warn them I'm about to unleash, warn them they have to the count of 5 seconds to leave.
Imagine I'm an evil criminal doing a house raid. I hear a voice that tells me to stop. I take my Tec-9 and unleash an entire mag in your general direction. Why? Because I don't care about neighbors or backstops.
You can't just fire/yell at a noise that you heard. It makes no tactical sense and it might get you: #1- Sent to prison or #2 - Killed. Target ID is essential.