For plinking: Depends on the range you plink out, .223 is limited to about 600m of solid ballistics, though you can go out to 800-900 with the right equipment and practice. .308 is good all the way to 1000+. All lot of this depends on the rifle of course. A bone stock FAL and M-4 aren't 800m rifles. Cost wise .223 is cheaper.
CQB/Home Defense: At these closes ranges, it's a toss up. A .223 might over penatrate less, but it'll still over penatrate. Both will put a man down properly placed, and both have enough energy to turn multiple marginal hits into a serviced target. Realistically which ever platform you handle better and can react faster with is the best. If you have a faster first round time with a .308 use it over a slower .223. Followup shoots only count if you're not down and out too. Also at those distances followups from both a .308 and a .223 are about the same in a practical view (not countings 1/100ths of seconds and such).
SHTF: Are you bugging in or out? If bugging out, then a .223 is usually lighter, and you can carry more ammo. It's effective on all game smaller then medium deer, and with good placement is effective well into the elk sized game (remember, a .22LR has taken the African Big 5, it's much more about the shooter). As a long range anti-personal cartridge, it'll be effective out to 600m or so with the right weapon. A .308 is heavier and will give you less carry capacity. It is effective on pretty much all North American game. As a long range anti-personal cartridge, if you have the right rifle and the right skills, 900m+.
If bugging in, ,.223 is probably cheaper to stock pile. Both calibers will be equally effective in maintaining security around your residence unless you have 600m+ lanes of fire. .223 ball will penetrate most things fairly well, as will .308 ball. The edge probably goes to .308 in straight barrier penetration.
Overall, either one is a fine round. Find what you enjoy shooting more, and are more proficent with. Then purchase accordingly. If you end up with an AR and FAL, the folks here will be more then happy to take the unused one off your hands.
-Jenrick