Keep in mind that no matter what you choose they are all going to go through walls and end up in the neighboring apartment if you miss (and sometimes if you dont miss). Yes each one will preform differently, but the bottom line is walls are softer than humans; so if you want to kill humans you have to accept the fact that you can kill walls too.
Personally one thing bothers me about long guns and home defense, the fact that they are long can make weapon retention, operating doors, helping loved ones, multiple times more difficult.
When making the purchase be sure to consider what else you want to do with the weapon. Most of us dont have the luxury of having a strictly home defense gun. If gettin out on the weekends and shooting a AR with your buddies sounds more appealing than going out and shooting a shotgun, then maybe you should seriously consider an AR.
Shotgun, pistol, and carbines are all effective home defense guns, in the right hands. Buy the one you that you will get the most trigger time behind. Just a thought.