I define long range shooting as 1,000-1,300 yards.
I would not be selecting an AR-10 if this was the goal. A 7-08 would be a great choice. But for a 7-08 to fit and feed out of an AR magazine means the high BC bullets desired for long range will have to be seated deep in the case. This will reduce your case capacity (i.e. less velocity), and the bullet will have a long jump to the rifling.
On the other hand, the 6.5 CM round you can seat the bullet out long and still be close to the lands while feeding out of an AR mag just fine. And, the 6.5mm bullets have a high BC and are lighter and can be pushed faster than a 308 or 7-08. For this reason, I would select an AR in 6.5 CM, if 1K+ yards was the goal.
The 308 in an AR will be running out of gas around 900-1000 yards, and may not make it much more past that. It will have much more drop and wind drift than the other rounds. I absolutely love my AR-10 in 308, but it is not a 1K+ rifle.