How heavy is that AR? Carrying around a heavy gun gets old real quick. Not long ago, one very knowledgeable hunter and gun writer with a lifetime of actual hunting experience suggested that a rifle and scope of 8 lbs. was ideal.
He was thinking: heavy enough not to punish you with recoil and light enough that it could be carried a long time. The last thing you'd want to do is to hike around elk country with an heavy rifle. It's tough enough doing it for deer when the terrain is gentler.
I agree that a Remington 700 in 30-06 would be ideal. If you insist on a .308, that would be fine, too.
I'm guessing that for the price of that AR, you could buy a Remington 700, a Remington shotgun 870, and a muzzleloader. I looked up the prices and could get all three for $1000 at a big chain type store.