I have never hunted elk or moose, but they are both on my list. I have asked many, just like you are, and the most common sense answer I get is .30-06.
It sounds like reliable knock down power (I have talked to many hunters that could not get a kill with a .270), and while many like the 7 mm mag better they know they can pick up .30-06 anywhere they are. A lot of stories out there of needing ammo, and having limited choices where they are at. It seems like everyone carries at least some .30-06.
Of course my rack holds a .270 and a 300 short mag. However, .308 and .30-06 are both on the wish list ... or should I say lust list.