"Seems to me that the 308 would be a more accurate round."

All other things being equal, perhaps that is true, but the fact is neither all guns nor all shooters are equal. I expect that the greater portion (for most of us average shooters) of error lies with the shooter first, with the cartridge and firearm following after. I expect that most factory cartridges, with most factory firearms, in the hands of a competent shooter, will be quite sufficient for hunting applications.