Either of your choices will work great with nothing lost going either way. They are both proven winners for deer, antelope, and elk.
If limited to just deer and antelope, I prefer the 6.5 MM bore diameter to the others, with the 6.5X284 and the 264 Win Mag getting lots of field time. I also like the 6.5X55 Swede. For something soft skinned but a bit bigger like elk, I especially like the 7MM Mag with ~160 grain bullets.
But again, either of your two choices are great options.