I truly wish people would stop using the term "stopping power". There is no such thing. Even the FBI says the term means nothing. They also state that a "one shot stop" is fantasy unless the individual is hit in the cranial or spinal cortex region. Even a heart shot, regardless of the caliber, will not guarantee a single shot stop. Shot placement and penetration are the primary considerations. A round to the brain with a .22LR will kill you as easily as a .44Mag to the same spot.
You carry what you can shoot comfortably. You practice with it. And you buy the best ammo for its intended purpose. Even if it is the lowly .22.
Start on page 7. This is enlightening for those that don't already have a closed mind on the subject:
http://gundata.org/images/fbi-handgun-ballistics.pdf