a .270 or 30-06 will both adequately take down elk at 300 yards. both can be used for moose. neither kick all that hard, making them easy to shoot.
theres no reason to kill yourself needlessly with bigger bores, if thats not your cup of tea.
that being said, i myself have a .270, and at 300 yards i would have to have that nice broadside shot on an elk to feel comfortable. i might have to exercise some patience with that gun, but i wouldnt hesitate to use it

brad