I seem to recall a program on one of those outdoor channels awhile back about hunting red stags in New Zealand - looked similar to sheep hunting out West, and looked like a long shot was a possibility. For that reason, I would lean slightly toward the .270. They are very popular here in the western states, and the 7MM-08 is not. One of the local gunshops had a nice 7MM-08 sitting on the shelf for years and finally sold it on the internet to someone back east. Not that they are bad . . . but it's likely no coincidence they aren't all that popular out here either.

And since you are buying a new gun and they all cost about the same with respect to caliber, I would look at the .270 WSM. Recoil is hardly any greater than the regular .270 and there are some great factory loads available - particularly the 140 Accubond.