I did a survey of a few calibers (including 10mm and .357Mag) some years ago of all the commercially available ammunition from companies who posted specifications for their ammunition online.
Comparing 10mm to .357Mag reveals that they're pretty similar by any measure of performance you prefer.
.357Mag has a slight energy advantage over the 10mm with the light bullet loadings and has slightly better sectional density in similar bullet weights due to the smaller bullet diameter.
10mm has a slight momentum advantage over the .357Mag with the heavy bullet loadings, seems to be able to handle slightly heavier bullets and has a slight diameter/caliber advantage.
The two things that are clear are:
1. These two cartridges obviously top the service pistol class in terms of raw performance.
2. Neither caliber begins to match the capability of the .41Mag or .44Mag calibers. It's common to hear the 10mm compared to the .41Mag, but that's not because the 10mm is that powerful, it's because some ammo makers have chosen to offer very lightly loaded options for the .41Mag caliber.