Hrrrm. The Soviet round is 7.62x39, the .308 is 7.62x51, and the 30-06 is 7.62x63. I notice no one is saying the Soviet round can be amped up to beat all .308s, yet the case length difference is the same. (I do realize it is a percentage thing, but it is still a valid point.)
As I recall, the .308 was developed as a more friendly to semi-autos cartridge to duplicate the ballistics of the original 30-06. Modern 30-06 is amped up above the original, probably due to the same powders that made the .308 equal to the original loading.
While it is possible to load .308 to meet 30-06 performance, it is akin to loading 38 Special up to 357 Mag levels. Yes, it can be done, but, for most commercial ammo, the 30-06 will outdo the .308, from what I understand.
Shot placement, no matter the gun, is penultimate. However, mitigating factors; wind, range, rifle rest, obstruction of view from natural objects, light, other animals, temperature, and last night's bean dip giving you gas all will play hell with your shot placement. This is why 'using enough gun' is important. I've chased enough other hunter's deer to learn that bigger is better, to a point.