The .30-06 is the greatest rifle round of all time. Mainly because it was the primary caliber for the greatest piece of military equipment ever designed: the M1 garand.

Either round is excellent. I'd prefer a .30-06 if I were hunting Alaska, other than that its a coin toss. The greater accuracy of the .308 is literally negligible unless it is a competition-style rifle in the hands of someone much better than 99% of all hunters.