For quite a few seasons the .300 WM has been my favorite elk and mule deer cartridge. I have used the lighter bullets out of a .300 WM on medium and larger game but I always thought the 180 grain bullet was a better match for elk. My rifles also normally shoot slightly tighter groups with hot 180 grain loads than they do with hot 150 grain loads.
I do not think it matters much which bullet you choose for mule deer with the possible caveat that at lower impact velocities I have not been pleased with the mono-metal bullets expansion.