The correct answer, as many have opined, is both. At long range the AR gives sustained fire power, rapid reloading and will penetrate armor below level III. Also the AR is easier for someone with a less robust frame to use, i.e. my wife.
But, from a defensive standpoint at close range the shotgun is best. If you are defending your home from a mass of protesters attacking your property, a 12 gauge loaded with 00 buck will plow a path through any group. My home defense shotgun has four in the tube and one in the chamber. Thats a lot of plowing.
There is (and this is just my opinion) another advantage to the shotgun. Adrenaline takes over in these situations and untrained (even trained) people tend to miss with ball ammo. I told my daughter to point the shotgun at the knees because if you jerk when pulling the trigger you will still stay on target. If you fire straight and true they will be laying on the ground screaming for their leg back. If you jerk a little you get a groin or gut shot, jerk a lot a lot you get chest or higher.
Doubtful in a defense of property situation you will start out shooting at long range. Shoot someone even a 100 meters out, not yet threaten you or your property, and you get a free pass to prison. Thin the herd with a 12 gauge then switch to the AR for anyone not interested in running away at that point.
I totally agree with you. Saved me having to type all that.