go on UTUBE and find videos..remember that a 556 will go thru walls
A 12 gauge slug will punch a half inch hole through over two inches of solid wood...
An AR is a great home defense weapon, and while, yes it will go through walls, as a good guy, you cant shoot through walls. You cant see your target. Bad guy doesnt have that constraint. But while the 556 or 223 round will go through a wall, it will likely lose both energy, stability, and direction by doing so. Even small bushes can deflect a 223 round enough to miss a target at relatively short ranges.
A shotgun is an area weapon, and while many say its the best home defense weapon, it comes with constraints. Lots of training involved in using a shotgun for a hostage like situation where friendlies are mixed in with your adversary. If an intruder grabs your kid, are you going to use a shotgun? I'd rather have the carbine.
Double ought buckshot will go through Sheetrock at close range like a knife through butter.