The 357 and 10mm are pretty similar on paper but in reality they are different. .357 is faster and lighter, generally has a more rugged bullet because it’s a 357 and people run them pretty hot for hunting purposes. The 10mm is heavy and slow by comparison
You are looking at the wrong loads.
I think the hotter loads in either 357 or 10mm are more potent than needed for SD against 2 legged predators. The mid level 357, hotter 9mm, standard 40 S&W or most 45 ACP loads have all proven to work about as well as any handgun load will work.
But if choosing a gun for protection from 4 legged predators the best 357 and 10mm loads are pretty comparable on paper. You can get a 200 gr hardcast from either out the muzzle at 1300 fps from a 4-4.5" barrel. The 357 load will have a little better SD and should penetrate a little more. The 10mm bullet a bit more diameter.
I made the move to a Glock 10mm pistol to serve that role over 20 years ago. My 4.5" Glock is shorter overall than my 3" Smith 629. And significantly smaller than any 4" 357 revolver. More than a pound lighter too. For performance that close I'll take the smaller more compact gun holding 15+1 rounds vs 6 rounds every time for a defensive handgun.
But hunting isn't Self Defense. If I were inclined to handgun hunt I still give the nod to a magnum revolver with a 6" or longer barrel. The longer barrels add some speed and will take the magnum revolver rounds into a category the 10mm can't reach. There just isn't much difference between 10mm and even 44 mag when the 44 is fired from a 4" or shorter barrel. The longer barrels along with better triggers usually mean better accuracy from the revolvers too.