As far as ballistics go, both are almost the same diameter. And you can get .357 and 9mm bullets in similiar weights. So, the difference is in the cartridges and the pistols that fire them.
A 9mm Parabellum is a relatively high pressure round, and the pistol designed to shoot them is relatively compact and light weight. So charge vs bullet weight is constrained to a fairly narrow range, making the 9mm a little less versatile that the .357 magnum.
A .357 magnum is a medium to large frame revolver, designed to handle everything from a mild mannered .38 target load, to some really hot loads pushing bullets that are a bit heavier that what a 9X19 can shoot with any useable effect.
With the .357, you can stuff a 160 JHP on top of a pretty hot charge and let physics take care of the rest. With a modern bullet, you're gonna get pretty good penetration and expansion (as far as a 160 gr .357" diameter bullet can expand anyway).
But, that being said, I suspect it'd be really tough to say if any handgun is consistently any more "deadly" than any other. It just depends, ....mostly on the skill of the user.
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On that same note, and interesting bit of combat lore is that one of the favorite handguns used by military special forces is(or was at one time) a suppressed .22 cal shooting subsonic ammunition.