I'm going to go with "neither".
I'm sure .357 and 10mm are both adequate for killing a black bear with a well placed shot.
I'm also sure that a well placed shot is largely a fantasy-event in an actual bear charge (between the body alarm response, and the fact that a bear moves very very fast). There are reasons why people who make a habit of hunting especially dangerous game in close quarters tend towards monstrously huge magnum rifles (rather than the minimal calibers which might work with a well placed shot).
If your life is actually in realistic danger to a black bear, consider selling/buying firearms to best suit your protection.
as much damage as possible within a given carry size/weight.
immediate ready-to-fire operation
1) .44 magnum 4" revolver: reliable, powerful, no safety fiddling, can use .44 special for home defense/practice.
2) Glock 21 with .460 Rowland conversion: lightweight, reliable, powerful, no safety fiddling, can swap barrel/spring to revert to .45acp for home defense/practice. (or a .460 1911, if you practice till the safety is an automatic reflex that takes zero time while drawing).
Or get a mossberg 500 18.5" 12ga. (6-shot, synthetic, pistol grip, alloy receiver). It's certainly heavier than a handgun (somewhere around 6lbs if you keep to all the lightest options), but handguns don't fire 3" 12ga slugs, and the longer sight radius will result in superior accuracy vs. a handgun, especially under stress.
Beyond that, make it a gun that "points well for you" so that you can acquire sight picture and start firing as fast as possible. And has a good trigger which you are intimately familiar with, so that you can have the best chance of squeezing off accurate shots in a situation which will greatly interfere with your accuracy. Practice with it, a lot. And get a holster which allows you very a smooth and quick draw.
Personally I'd go with the G21 with .460 rowland conversion. It's the lightest of the bunch, hits arguably harder than .44 magnum, converts back & forth to .45acp very easily. But I have a glock bias, and I'm extremely proficient with them.