There are a lot more options in .357 firearms so barrel length becomes a big variable when comparing the performance of the .357 to the 10mm (which has a minimal range of weapons to choose from). All other things being equal, with proper loads, I’ve always thought of the 10 as bridging the gap between the .357 and .41 magnums.
With the heavier bullets (165 grains and up for the .357, 180 grains and up for the 10 mm) both have plenty of penetration to use for defense against bears.
As I have collected incidents of pistols being used against bears, the primary factors, for a pistol of 9 mm or greater power, seem to be a willingness to shoot, knowing bear anatomy so as to shoot for vital areas, and to keep on shooting.
However, there have been a number of documented one stop shots of Grizzly bears from 9 mm to .44 magnum.
The number of documented bear attacks and defensive uses with pistols are so small as to make caliber comparisons of little value.
My suspicion is that many successful uses of pistols to defend against bears, especially black bears, are never documented, or, if they are documented, are never reported to the public.