In the last week, I've been qualifying my rifles in .270/.308/.30-06/.375 H&H. I have all shooting under 1 MOA with appropriate handloads. I would go with .270 Win AccuBond 130gr with whitetail, 140gr with mules/elk, .308 Win 150gr w/ whitetail, 165-168gr with mulies and elk, .30-06 168gr with anything but brown bear/moose, .375 H&H with brown, bear moose, .375 H&H with anything I couldn't adequately plan for and be comfortable that good shooting, inherent accuracy of my rifles, my shooting ability would take anything I'm likely to hunt inside of 300 yards. As a personal choice, I will not take a shot at more than 350 yards, because I want to ensure I can make an ethical shot successfully. YMMV, and better shots than me may want to go a different way.
My thoughts,
Cheers,
Harry