I was waiting for someone to mention Marshall & Sanow. Since no one did, I will - at the end of the day we need some data to answer OP's question. Of course there was a lot of arguing about it but AFAIK that's the only data we got...
Now, as long as you believe they've done a good job (I think they have), the answer is right there in their tables. Best 357mag load - 96% one shot stops; best 38spl+P+ load - 80%. That's a big difference
If that were one of my student's thesis papers I'd have given him a C. The method of data collection was poor. They exclude data where there were multiple com hits with failure to stop. While their apologists argue, "but it's real life data" my reply is, "so is all of the useful data on failures to stop that they simply threw out."
I am not impugning their motives, just their data collection methods.