"Big game hunting?" The 10mm is legal for 'Deer sized game' in almost every state. I'm surprised the .357 is legal for deer in Oregon. "BIG game," like bear, it is only designed for a desperate fall back when no other arm is available, and in the right hands will stop a bear (documented cases for proof)! The major problem being, most shoot the 10mm with less than FULL HOUSE loads and they may as well be using a standard 40 cal. The full 10mm is more comparable to the power of the 41 Magnum, not the .357. Only the Buffalo Bore brand of .357 ammo approaches the energy levels of the 10mm and still uses a smaller bullet, and those pressures probably overwork the revolver, and possibly the semi-auto.
Not many folk 'hike' the mountains or "bear woods" with a 30-06 or comparable long arm. Though there are more powerful handguns than the 10mm, they tend to be quite heavy with almost uncontrollable recoil, and if you want something that heavy to pack around, you may as well carry a rifle! YMMV, but as you say, "if I were hunting the bear with a rifle, then I might have one of these as a last resort," but having no rifle while hiking, or just enjoying a day in the woods, the full house 10mm, w/10-15 round magazines, just might save the day! BTW, states that limit magazine capacity for a handgun should be shunned, and at the first opportunity the clowns making such laws run outta-da-state!