.357 magnum is much hotter than 9mm, especially from short barrels. Chronographed from the 2.5" barrel of my S&W Model 66, Winchester's 145 gr. Silvertip (a superb defense load, BTW) travels at 1241 fps. 9mm can't begin to match that. The 147 gr. 9mm +P flies at about 1050 fps from a 4" barrel. From a 2.5" barrel that 9mm 147 gr. +P may drop to as low as 975 or so... no match whatsoever to the .357 magnum. And the huge case volume of .357 magnum gives great benefits of lower pressures and greater margin for error in loads than the tiny case volume of the 9mm case. Yes, .357 and 9mm share the same bore size and similar bullet weights, but the other differences between the calibers are huge.
Of course, in the above paragraph, I was just comparing velocities, which isn't nearly as predictive of "stopping power" effectiveness as terminal performance metrics are (penetration & expansion). 9mm does pretty well these days in terminal ballistics, but even with the best designed Gold Dots and other engineered bullets, 9mm cannot equal the terminal effectiveness of .357 magnum.
That said, the benefits of 9mm's semi-auto action, lighter triggers, MUCH higher capacity and much quicker reloads gives 9mm quite a lot to crow about. Despite the power differences between .357 magnum and 9mm, for carry gun/defense purposes, I would choose a modern 9mm semi-auto pistol over a .357 mag wheelgun simply for the benefits other than power that 9mm offers as compared to .357 magnum.