One of the great things about America is that you can think whatever foolishness you like.
A .357 may or may not have more "stopping power" than a 9mm fired from the same range and (since accuracy is more important than caliber) hitting exactly the same target. Your statement is categorically incorrect, however, because you have not addressed the variables of (among others) barrel length, bullet weight, muzzle velocity and expansion characteristics of the round. You've also ignored the 6 or 7 round capacity of the .357 compared to the 15+ round capacity of the 9mm.
Hornady makes good ammo. Whether or not it is the best choice for a particular person firing a particular weapon is quite debatable. I like the Hornady Critical Defense loads for my wives Bersa Thunder380. I hate them in my Ruger P95 and S&W Model 66. After actually testing ammo, I carry Hydroshocks in the .357. The 9mm is loaded with Glaser Silvers, with the spare magazines holding Black Talons and Hydroshocks.
No. It's not.
At 5 feet I can ask you which nostril you'd like the bullet to go through, so the caliber is pretty much a moot point.
View attachment 18904
This was shot today. Ruger P95. 115gr FMJ. 6 yards. Single fire. 15 rounds.
Now, here's a test for you. Is a 15 round grouping such as that a good thing for personal defense shooting? Why or why not?