Well, the OP is asking about an AR and stated that HD would be one of it's uses. If you don't think an AR even belongs in the toolbox for home defense, why are talking about which AR the OP should get when one of the uses includes home defense?
As for the theory behind that question...
There are pros/cons to each weapon type for HD, same as any other use or choice. Before even going down that road we would have to know what other firearms the OP had or intends to acquire, where he lives, what his training/experience/knowledge on the subject is, who else lives with him, who else might use the weapon, etc.
For ME, an AR can be considered for home defense because it is light, maneuverable, has a high capacity, good effectiveness, low recoil/fast follow up shots, transitions quickly between targets, can defeat soft armor, etc. It could also transition very nicely into a use outside of the building. Limitations include price and muzzle flash/blast.
Handgun advantages include the ability to use with one hand and the ability to keep/store them in more locations. Limitations include lower effectiveness and a greater skill requirement to implement effectively.
A shotgun's advantages would be price, reliability (basic pump), and effectiveness in stopping the attacker once struck. Limitations might be recoil and weight as well as ammunition capacity.
Note that when comparing common defensive ammunition the pistol is actually the one that is likely to penetrate the most interior walls and that anything capable of reliably stopping an attacker is going to penetrate interior walls.
http://www.theboxotruth.com/
