For general use, the .223 has got quite a lot of advantages over the .308:
You can carry the same number of rounds in a smaller bundle; or more rounds for a given size bundle. BLS of soldier is about 100 rounds of 308 vs 330 rounds of 223.
Killing power is pretty much the same according to gummint tests.
Ammunition is significantly cheaper so you ca shoot more for a given amount of $$$.
Reloading is also cheaper, uses about 1/2 the powder of a .308. Smaller, cheaper bullet, too.
Accuracy is about equal, however, I would guess the average AR15 will outshoot the average .308, given the diversity of types of weapons chambered in the latter: bolts, pumps, levers, old military clunkers, etc., etc.
Best regards, whatever your choice!
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Yankee Doodle