Starman: I live and Hunt, a lot, in SW Montana nowadays, and have used both calibers on game from Antelope, Deer (3 kinds), Black Bear, Mt.Goats and Elk.
The "nowadays" comment is emphasized because Grizzly Bears are expanding both in the areas they frequent and in their populations anymore.
So I would give the edge when Hunting in my neck'o the woods to the 308 and the wonderful 165 grain Nosler Partitions I use in mine.
The 270 Winchester is a wonderful cartridge and I love all of mine but would rather go with the 308 and proper bullets, when in Grizz country.
Could not tell from your header where or what you will be Hunting.
Good luck whichever you choose.
Long live the 270 Winchester!
Hold into the wind
VarmintGuy