A mature Shiras bull moose is slightly smaller than the Eastern moose and my friend and I used our old trusty 30-06s without any problem on those. They can be taken with less potent cartridges but IMO I would rate the '06 as minimum. I'm sure there will be some that disagree. But whatever you choose you need a good stout bullet to penetrate deep into the vitals and/or smash some bone.