If you load the 155 grain Sierra Palma match bullet, you can stay above transsonic out to 1000yds in the .308. Something about the higher M.V. and a superior ballistic coefficient gets it there.
My Sendero .300 Win Mag gave me .70 MOA out of the box, with a Simmons scope. With some smithing and a better scope, it might do better. Pillar bedding on these is not necessary, given the aluminum block bedding that's built-in. Accuracy potential is in the load, the trigger, the bolt lugs, and the sighting system.
.300 Win Mag is getting to be quite popular lately-- cartridges are readily available. But it's expensive to reload for. Much easier to find .30-06 Match.
At 600, .308 is all right.