I would second the 300WM with good 200 gr. bullets and your rifle zeroed for the 200gr. I would not recomend carrying two different bullets weights arround since your rifle will only be zeroed for one (unless your rifle can shoot 180s and 200 with the same zero). Two years ago my brother got a nice brownie, smaller sized guy (like the ones you'll see in Sheep country) and it went down with one good shot from a 300WM with a 200gr. bullet. You'll be better off for the sheep with the 300 and as the others said you have a guide for the bear.

Have a great trip!