I would go for either as for most hunting situations neither you or the game will know the difference.
Find the gun that "feels" right and go for it.

Having said that if moose, elk or grizzly hunting is in your future then the nod would go to the 30/06. This is where the heavier bullets shine.

I personally prefer a 308 over a 30/06 but that is only because I was able to get a smaller, lighter rifle in 308 then 30/06

You may want to also look at the 300 wsm if you plan on hunting larger game