SHTF? 5.56/.223. Hell, ontop of that, get yourself a .22LR upper or a ciener conversion for quiet small game gathering purposes.
If you want the gun for SHTF, I'd really say it depends on your area. If you live in a flat wide open area like the SW or central United States, .308 starts making a lot of sense. But, if you live in the east amongst urban sprawl or just tight woods .223 makes the most sense.
What really does it for me about .223 is in a SHTF scenario, if your bugging out, or even bugging in, there is no logistics chain to support you. You aren't part of a war machine. You get what you carry, and thats about all she wrote for practical purposes. Carrying in either case one of the two most common cartridges in the United States is wise though because you may happen amongst some ammo, but you can't count on that. In the terms of sheer weight you can only carry so much, and pound for pound you get almost twice as much .223 ammo. Also for SHTF a cartridges adaptability is paramount, because you don't have an arsenal to choose from. Most likely you'll have one rifle, or more importantly one caliber, and that caliber has to do everything from bunnies and dogs to people and deer, to whatever unforeseen situation arises.
Stopping power wise, I think more ability to make relatively softer hits trumps less frequent harder hits...to a point. I don't advocate using a pistol caliber carbine but in the scheme of things .223 is anything but. Its a very destructive round out of a 16 inch barrel out to around 300 yards. It still way better then shooting someone with a 9mm at 10 yards out around 500 yards.