Caribou are not tough animals. The .308 will do fine espcially if it's noticably lighter than the .338. Caribou hunting often involves a lot of walking.

I hunt woodland caribou in Newfoundland (resident) and this year I seriously considered sighting my Dad's .30-30 for fifty yards and using that since in the past all my animals were taken well within that range. In the end I said the hell with it and took my scoped .30-06 again.