Comparing a bolt action .308 to an AR chambered for .308 is apples and oranges. Too many differences. But as for the cartridge itself, you're right; the distance and ballistics will be comparable.
Can't speak to that particular brand of AR, but a good AR with optics for $1k is not a bad deal at all, granted the firearm is reliable and complete. Good brands of ARs in .308 usually run about $1,200.00 minimum fully assembled, and that's almost never including optics/scopes.
On a side note, don't be too quick to dog the .223 caliber ARs. They may not have the reach-out-and-touch-someone-at-450+yards range of the .308, but realistically speaking, if you're using it for hunting, you're probably not going to come up on too many opportunities to take your prey beyond 200-250 yards. Also, the ballistics of a .223 on pelt damage and meat destruction are far lower than that of the larger .30-caliber cartridges. Not to mention, carrying a standard load of .223 ammo will be consistently lighter than that of the .308.
If you're thinking of personal defense or anti-zombie armaments, I'd still suggest the .223 clambering
