There are those out there who say they have this or that brand of AR, and can shoot to those ranges and then some, and shoot MOA all day long...
Maybe...I haven't seen it yet, but there may be a few...uh-huh
I have a bolt gun in .338 Lapua, and on a good day, when my eyes aren't feeling as old as they really are , I can hit anything out to 1600 yards (about as far as I can without driving out to the desert on the eastern side of the state), with ease. Price of the gun at this point, without optics on it, or bi-pod, you are looking at close to $6500. Add in the Schmidt & Bender scope, the bipod, match ammo, etc, etc, etc....you could easily have bought a Barrett .50 M82.
But....it weighs a bit less than the Barrett, too. (Not much, but a little )
It also costs a little less per round, too.
You can probably find a set-up now, Barrett just put one out, Armalite has their AR-30 in .338 now, for a bit less than what I have in mine. Or you could look at Accuracy International, Sako, etc, and 2nd mortgage the house, or pimp the wife and kids - to afford the habit.
I would say to do what you want to do, and do it competitively, you will need 2 different set-ups.
But if you are just looking at something to have fun with and compete out to 600 yards, you could feasibly do it with one lower, and a couple different uppers on an AR. A good 24" upper, free floated, 1:8 twist, a good scope, match ammo, with a match trigger is capable of MOA out to 600 yards.
Then when you are at home, pull the two pins and slap on your tacticool-home-defense-zombie-blaster upper.