All else being equal the larger caliber wins. You are comparing a light for cartridge bullet with a heavy for cartridge bullet though. In 357 the go to SD bullet is the 125 grain JHP.
I prefer a 140 Speer and I load it to 600 ft lbs from a 3" gun. It's very accurate, better ballistics in a short barrel than can be gotten from the lighter 125 grain stuff, which really need at least 4" of barrel. The 140 Speer a VERY accurate bullet, works well in my .38s as well, though I sorta prefer 158 grains in .38 special.
I prefer a 165 cast gas checked SWC at 1470 FPS from a 6.5" barrel for hog hunting. I wouldn't hunt hogs with .40, a little light IMHO and more range limited. ,357 offers more energy, better SD, for medium game and does a good job. I've taken hogs to 60 yards with it. I also have a pet 180 XTP hunting load, 1402 fps/785 ft lbs from my 6.5" Blackhawk. That load is 5" high at 50 for a 100 yard zero, pretty flat shooting for a standard handgun round.
Nothing wrong with the .40 for self defense, I just prefer .357 as a caliber, much more versatility and I'm sorta a revolver preference kinda guy.
Head to head, the 10mm is a better comparison to .357, can match energies of the hottest .357s with a bigger bullet, though I'm not sure if it can match the heavy .357's sectional densities, which is important for penetration on game. I haven't looked at the 200+ grain .40 caliber stuff. It's probably close enough, though.
But, I'll trump your 10 with a .44 magnum.