ORIGINAL: Aught Six
I'd feel better having a .308 in just about any combat-type situation, but the .223 does seem to make more sense in this case. As mentioned, you'll carry more weigh per round of the .308, and mags are difficult to find or replace. For a civilian who doesn't have Uncle Sam stocking gear for him/her, you'll need to get mags and gear wherever they may be, whether looted stores, fallen citizens/criminals/police officers, etc. You'll be lucky to find a 10 round AR-10 mag no matter where you look.
The .223 is also adequate for home defense and your average suburban treet battle. Unless you're against people in armored cars or high-level ballistic vests, the .308 would most likely be overkill. And you can always keep a few mags of SS109 handy (green tip).
Now, if I had some kind of home base and were living off the land, a .308 would have it's advantages with big game.
Aught, it sounds like you live in a very tough neighborhood!
Caldoc