Well, the .308 and .30-06 were both military cartridges. The bullets they use are fairly identical, and in the military loadings, they perform almost identically. The .30-06 is about .5 inches longer than the .308, which in commercial, or bolt action guns, can be loaded a little hotter. The .30-30 was Winchester's rimmed cartridge that was one of the first to use smokeless powder. It is a bit less powerful than the .308, due to reduced case capacity, less powder and lower velocity. Any of these three rounds should work great on deer up to about 200lb plus.
As for using your AR for deer hunting, check your state laws regarding the minimum caliber allowed for hunting. In some states, you can't use a .22 (.223 or the like). And in some states, you cannot use a rifle with a magazine capacity of more than 5 rounds.
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