My uncle, who lived in the bush of Alaska from 1973-2000, only hunted with a .243. He told me in that time he killed probably 20 or more grizzlies with his trusty .243, not to mention all the moose and other animals he got. It's all about bullet placement. Size doesn't matter if you hit where you are supposed to.
So based on your uncles experience why is your handle 338ultramag , shouldn't it be 243mag or something along those lines ?