For Elk-Brown Bears, I'd say a .338mag, ideally the .340 Weatherby.
Of those 3, personally I'd pick either of the WSM's, and because you're talking moose, elk, big game...I'd lean towards the .300wsm
The 270wsm and 7mm RM IMO are kinda the same cartridge, compare velocities/energies I think the 270wsm may even get the edge in velocity, if not they're very close.
I think my debate would be which one of the following...?
.300wsm
.300win.mag.
.338win.mag
.340wby. (225gr.TTSX@3100fps, BC= .514, SD=.281) and shoots as flat as a .270
the .340saying should be..."shoots as flat as a .270, hits as hard as a .375H&H"
*btw any of these 4 would get the job done well!