One caliber many have surpassed is the new 325 WSM. You could use 180 gr. bullets for White-tail & Mulies. Then step up to the 200-220 for the larger animals. At the local gun shop the owner states Winchester will be bringing out a fail safe load for this round soon. The Fail-Safe will take the large bears with good shot placement. Even large men can become recoil sensitive.

The other thing that most say is to stay with the 30-06 and you could use it for all but the big bears. Also, the 06 is more potent today with the High Energy and Light magnum loads available for the 30-06.