If long-range (anything over 400yds) is the game, then I'd opt for the AR in .308....... even though many service rifle matches shoot the 5.56 at 600 yards.
With the .308, ammo is higher, especially if punching holes is the main game, but you do have much more in the power factor arena for things such ad hunting big game and bucking the wind at longer ranges.
*As a side note, my next purchase, pertaining to my own newly-acquired-first-AR, is a .300 AAC Blackout barrel, to be followed by parts to assemble a complete upper (as funds allow). After toying with a friends rifles in this caliber, and as ammo becomes more available, I like what it offers in the AR platform: short-to-mid-range .30 caliber, with a wide variety of bullet weight options, at both sub and super sonic velocities..... all in a standard AR package.