Some well placed shots from a .22 has stopping power. If you are dead set on a 357 I would find something with a little more weight like Ruger's SP101 or S&W 686. Those sub 16oz snubbies with magnum loads are a handful especially to keep on target in rapid fire. Ever look into the 357SIG in a compact platform such as the S&W M&P liine, Sig Sauer, Glock etc. That cartridge outperforms the 9mm, 40 S&W and 45 at distance.
Ok... lets have a real look at "stopping power"...
First off I'll mention the obvious... any bullet, no matter how big it is, that misses has absolutely NO physical stopping power. None... nada.. zip. Can we agree on that?
Also... any bullet that misses carries with it the responsibility to be... responsible for where ever it goes. If that means it hits my car... you pay to fix my car. It that means it hits an innocent person a block away... you are in deep crap! Can we agree on that?
So.... in order to even talk about this magical thing called "stopping power" we first have to be talking about bullets that hit the attacker. Can we agree on that too?
Now....
The real world try to save my ass from an attacking criminal situation has absolutely nothing in common with farting around practicing at the range... unless your range allows you to shoot multiple targets while running backwards and sideways.. because in the real world no one stands in a perfect Weaver stance carefully paying attention to sight alignment and trigger control. In the real world people are shooting as fast as they can at a moving bad guy while back pedaling, maybe tripping over a curb and falling on their ass, as they try to get the hell away from the attack. There isn't time to carefully align the sights... there isn't time to worry about any "perfect stance"... hell.. the usual "stance" is ... moving! and might entail firing a shot with both feet off the ground. Anyone who thinks any different not only has NOT experienced a real world attack but hasn't taken the time to think through what an "attack" really is.
So... what caliber has the most "stopping power" in the real world? None of them and all of them. Because....
What it comes down to is very simple... what gun/caliber combination that YOU are able to empty firing rapid fire while moving.... and all the rounds hit center of mass... means each and every one of those bullets that hit had some measure of "stopping power". Only hits have any "stopping power"... misses don't help no matter how big the bullet is. Jeepers.... even a rocket propelled grenade (RPG) that missed didn't "stop" the attacker!
Ok... for me... I can hold all 11 rounds rapid fire (firing as fast as I can pull the trigger while I'm moving backwards on an angle away from the target) with a Glock G26 9mm that is comfortable for me to carry both openly and concealed. But... if I move to a G27 in .40 cal I will miss center of mass with one or two rounds. If I move to a larger gun no matter what caliber it isn't comfortable for me to carry.. so.. the Glock G26 in 9mm IS the best carry choice................. FOR ME!
Clearly.. for me... the 9mm is better than the .40 because I am more accurate with the 9 than with the .40. So... for ME... the 9mm has more "stopping power" than the .40 does. For the simple reason that I can put more 9mm bullets into the attacker than I can if I used a .40.
And so it should be for everyone. Take the time to experiment with different guns in different calibers and find the one YOU are able to keep all your shots in center of mass firing as fast as you can (that is what you will do when someone attacks... you won't just stand there taking carefully aimed shots!) while you are moving.
And that gun/caliber combination must come in a size/weight that YOU are comfortable carrying... because... if it isn't comfy to carry you will leave it home.
Oh... and please don't fall for the caliber elitist crap where someone says "x" caliber is best.. because.. the "best" caliber with the most "stopping power" is the one YOU can hit the bad guy with the most often under the worst conditions possible.
Remember... misses, not matter how big the bullet is, have no "stopping power" what so ever!
Edited to add....
My loving wife carries a .22 for self defense. Yeah... the lowly .22. But she can put all 8 rounds into center of mass while running (running!) backwards and off to the side. But... give her any other caliber in any other gun size... and she starts missing because of the recoil. So... because she does NOT miss.... for her... the caliber with the most stopping power is.... a .22.
Feel free to disagree.. that is what forums are for. But please understand... I'm talking about the real world... not blocks of gelatin or elitist caliber BS... the real world where only hits count and misses don't.