In proper hands, the .338 is a better long range round. It shoots heavier bullets, with higher BCs. Just using physics, it has an edge over the .300 Win Mag.
What's the highest BC bullet in 30 caliber?
Just using physics, including that of the shooter, the .300 Win Mag's a better choice. So proved in controlled conditions by the US Army tests. Why do you think the 6.5 calibers have been favored for accuracy over anything larger in long range shoulder fired matches?