You pose a really good question. Let's dig a little more.
Weight (lightest to heaviest) ammunition: (1) 5.56x45 NATO (.223 Remington); (2) 7.62x39; (3) 7.62x51 NATO (.308 Winchester). The lighter the ammo, the more you can carry.
Rifles or carbines (lightest to heaviest): (1) AR and AK, SKS pretty much of a tie with the AR maybe slightly lighter depending on configuration; (2) 7.62 NATO rifle will be heaviest.
Effective range and stopping power: (1) 7.62 NATO (.308 Winchester) is tops; (2) 7.62x39 is second; (3) 5.56 NATO (.223 Remington) is third.
Sights (iron and optical): With optical sights, things are pretty much equal among all three types of rifle. With iron sights, the best are usually found on the 7.62 NATO (.308 Winchester) and 5.56 NATO (.223 Remington). The iron sights on the AK and SKS are better than nothing, but not by much.
Resupply: (1) 5.56 NATO (.223 Remington) gets the edge here, (2) 7.62 NATO (.308 Winchester) is a close second; (3) 7.62x39 is third. The 7.62x39 is commercially loaded in the U.S. and there is a lot of commercial and G.I. surplus in this calibe about. However, there's not as much as the first two if the supply is interrupted or cutoff. Both first two are also available from law enforcement and military sources in the worst case scenario; 7.62x39 is odd man out.
NOTE: You should already be stocking a goodly supply of whatever ammo you intend to carry in your "bug out bag."
Being an old fuddy-duddy, I do like the old M1 Garand in .30-06 or .308 Winchester. Yeah, it's a real clunk in the weight department and you can't carry a lot of ammo (relative to the .223 or 7.62x39), but you can't top it for reliability, balance, and stopping power. True, you only have 8 shots in the clip before reloading, but which would you rather have: someone pegging shots at you with the M1 or someone pegging shots at you with an AK or AR. [The "mouse gun" is slightly better than the AK.] If you said AK or AR, you'll probably lose -- and definitely lose if you are a "spray and pray" kind of shooter.