Black bears typically aren't a problem unless you run into a mama bear and her cubs. If you see cubs, quietly back off to create distance. Cougars-or at least some of them-regard us as just another source of protein (and easier to catch than deer). Unless rabid, yotes typically aren't an issue.
You're looking at this as an equipment/hardware issue and it's really a software issue: your ability to accurately and rapidly place shots from an adequate firearm/ammunition combination. I'd hesitate to pick the Vaquero unless you can really do so by a rational measure. The .357 with proper ammo and a couple of speed loaders/speed strips would seem to be the better choice. 158/180 gr soft points by major manufacturers would be my choice. Beware the boutique loads. Perhaps one reload with 125 gr JHPs for the yotes.
Consider the weight of whatever you carry as an aid to developing your physical fitness and also the item that will keep you off the list of folks who end up as critter feces or getting rabies shots. Do spend some time with sources that can show you the vital areas of the various critters from different angles. Don't even think about head shots for a variety of reasons-unless it's through the open mouth aiming for the spine of a charging critter.
I carried an issue 10 mm for ~16 years. I wasn't impressed. If you're trying to rationalize a new toy, hey, it's your money. FWIW, a 158 gr .357 " bullet has the same sectional density as a 200 gr .400 " bullet, better sectional density than the much more common 180 gr bullet. In other words, much better penetration capability using commonly available factory ammuntion.