If you are hunting with a rifle and can't kill a bear with it, then your chances with any handgun are pretty slim.
And in all the testing I did with various handguns and assuming equal quality bullets, I would rate the 357 and the 10 mm as virtual equals, so pick the one you are most comfortable with.
Phil
I recall you have posted a pic of your wife in the cabin kitchen w a .357 holstered at her back?
180 HC in that?