I face the same decision. I'm going for the 6.8 Western, as IMO it's the best compromise of the three for long range hunting for deer and elk. More of a power/energy buffer for long range big game, flat shooting, availability of high BC bullets, less recoil than the larger calibers. I'm going to build mine on an ARC Mausingfield M7 action with 26" CF Sendero profile barrel... more velocity, less muzzle blast. I'm going to try for 9 lbs with scope and should have a very pleasant shooting rifle.
I think this is an underappreciated cartridge... as someone posted Hornady hates it because it is better than their 6.5 PRC or 7 PRC as an all around North American deer and elk cartridge. Witha 26" barrel it's faster than the .277 Sig Fury out of a 20" barrel without the higher pressure or muzzle blast.