Both rounds have their merits and are very capable of personal protection against rodents and man. Now a bear I'm not sure and truthfully don't really care to find out first hand. Maybe the bear spray and a change of underwear would be the better route in this scenario.
I guess one question would be your choice of firearm and barrel length. The shorter barrel does result in a diminished impact of the bullet. How many rounds of ammunition would you prefer to have available without the need to reload. Most wheel guns 357/38spl are 5 to 6 round capacity, where the 9mm could be as high as 17 rounds.
Cost wise for shooting rodents the 9mm would be the cheaper choice as to ammunition cost.
I guess my answer would be to choose the firearm that you feel most comfortable with in reliability, accuracy, and familiarity of function under pressure.
As you noted, the 357 has the ability to fire two different calibers of ammunition which is a nice feature. There are however a few semi automatics that will allow this same flexibility with the simple exchange of the barrel. Such as the GLOCK .40sw can also fire 9mm and 357Sig by only changing out the barrel of the firearm. Conversion barrels average $129 to $159 depending on your choice of barrel, such as do you want ported, threaded, stainless, blued and such.
Personally I have stopped carrying my M85 and now focus more on carrying a semi auto, usually in a .380(aka 9mm short), 9mm or .40sw. My choice of carry for any given day will depend more of the weather, plans for the day and clothing selection. I also like having more than 5 rounds in the chamber if needed, which I pray they are never needed.
So in conclusion, I didn't start any caliber wars. But, I also didn't help much in supporting either one of your choice over the other.
Have a Great Day,