Your question is a good one, and the answer is quite complex.
First- "stopping power"- there is no good definition that is accepted by everyone although many have tried. Some knowledgble people believe it is best to have a light weight, very fast bullet. Others, also knowledgable, believe a heavy, slow, deep penetrating bullet works best. To make matters more complicated your bullet speed will vary depending on the length of your barrel. It may be fast with a 5 inch barrel and a lot slower in a 3 inch barrel, even with the same bullet weight and powder charge.
Kinetic energy gives the bullet the ability to do work (expand and penetrate), and is highly dependent on the speed of the bullet. If all other factors are equal, a faster bullet should penetrate and expand more than a slower one.
The three most common semiauto calibers for self defense are 9mm, .40 and .45. The .40 came into being as a more powerful cartridge than the 9mm was sought because of perceived notions that the 9mm was too underpowered to achieve incapacitation in some circumstances. The .40 is a compromise in size and power to the .45 which many people find hard to grip and shoot well.
In actuality, the caliber and bullet weight and speed are all secondary to hitting the center-of-mass of your target under stress. There are many 9mm loads that work quite well now. Any of the above calibers is adequate if the shooter can do his part well. If you can do your part well with a larger caliber then that is even better. For what it is worth I usually carry a .45, but sometimes a 9mm with Remington Golder Saber HP's and I do not feel undergunned. Hope this helps.
best wishes- oldandslow