As factory guns go the 308 probably has the accuracy edge but tin a custom gun their equal , the 30-06 will probably give 100-200 fps with hand loads and will show this more noticably with the heavier bullets.
The 308 has ALOT more factory match type loads
Personaly I don't think that you would see a differance ballisticaly until you got out to 500+yds then I still don't think the animal would know the differance.