HouseofCash, the .308 was developed by the military after the second world war. The idea was to get .30-06 performance in a smaller package so the troops could carry more ammo. Loaded to higher pressure, with the then newest powders, it did give similar velocity with lighter bullets.
But the .30-06 performance was boosted by the ammo makers around the same time.
For a deer hunter, there is not much difference, but the .30-06 will always be superior, especially with heavy bullets because of the bigger case.