I don't know what or where your gonna hunt but I'd go with the .308, it's chambered in a wide variety of rifle types.

It's inherently more accurate than the .270, but there are many other factors involved in that regard.

If you reload there is a wider range of bullets available, and even if you don't there is a load of surplus ammo out there for practice and plinking.

And, skill with your rifle will matter more for hitting game at any distances than any extra velocity or muzzle energy.

"Lord, make me fast and accurate."