Comparing the top 357 Man Stopper, a 125 Gold Dot @ 1500 FPS, to the top 10mm man stopper, a 180 Gold Dot @ 1300 FPS, you find similar penetration but the 10mm has 30% greater expansion. So how is that insignificant within the confines of the OP's question?
If you do apples to apples, you'll get numbers that are so close that it's pointless to try to make something out of the differences.
In other words, instead of comparing a heavy bullet 10mm loading to a light bullet .357Mag loading, compare light bullet loadings in both or heavy bullet loadings in both.
The .357Mag will drive a 125gr bullet up to maybe 1500fps to 1600fps out of a 4" revolver while the 10mm will drive a 135gr bullet up to 1400fps to 1600fps out of a 4.5" bbl service pistol.
The .357Mag will drive a 200 gr bullet up to 1150fps to 1200fps out of a 4" revolver while the 10mm will drive the same weight bullet up to 1050fps to 1275fps out of a 4.5" bbl service pistol.
If you want to look at the 180gr bullets, you'll find that the 10mm maxes out around 1350fps while the .357Mag seems to top out at about 1300-1400fps.
If there are significant differences there, I'm not seeing it. The .357Mag looks like it might have a slight energy edge with light bullets while the 10mm may have a small edge with the heavy bullet loads. At one point I got exercised on this topic and did a complete survey of all the ammunition companies that publish ballistic data on the internet and did a comparison with all the available data I could find comparing the .357Mag and the 10mm. Basically it convinced me that the two calibers are almost identical in performance.
You can find differences, but they're only significant if you can make something out of 50-75fps here and 10-15 gr there.
I stand by my original statement.