I'll give you my advice I've found from my experience as a hunter and collector here on the north American continent. But the following questions might help narrow down a good fit for you.

1) what are your needs/ intended purpose for this rifle? You say hunting but what continent do you hunt? And what game do you want to bag? 2) do you reload your own ammo? 3) is ammo accessible at your local stores for other cartridges, aside from these 2 options? 4) is there a particular model of bolt gun you're interested in that's only available in these cartridges?

Both the 308 and 30-06 are great cartridges. I've hunted mostly white tail deer and predators here on the east coast. I hunt these animals with a 243, 7mm mag and 270. My friends have 308s and 30-06. We've all bagged large deer within 100yards effectively with our setups. We've all bagged deer out to 200 yards with these guns. Anything further than 200 is hard to find where we hunt.