I would say so. I don't believe there is anything that we could remotely call "stopping power." Rather, a collection of factors that contribute to whether a threat stops being a threat. Some of those factors are fully under your control (i.e. cartridge selection, barrel length, bullet design, etc.). Some are only partially under your control (i.e. shot placement). Most are entirely out of your control (i.e. your attacker's use of drugs, mental state, clothing, movement, etc.). As mentioned several times in this thread, Cooper's advice to carry the most powerful gun you can shoot well might be the best advice.
"Shooting well" is a subjective assessment, though. We can place objective metrics on the skill for qualification purposes but the design of the metrics is still subjective. There is no solid answer as to how fast and how accurately we need to shoot. More power means more recoil and more recoil means slower shooting. When that fact is discussed, there are inevitably tough guys who proclaim how quickly they can shoot their Super Deathblastomatic in .492 Vaporizer. Even if their internet claims were true, physics dictates that the same person could shoot a "lesser" caliber from a similar gun more quickly. We have to decide for ourselves where we are comfortable in the spectrum of speed versus power. It's important to remember, though, that handguns are not powerful; they are portable. What differences there are in power are generally minor and still on the low end of things. In other words, small gains in power can result in large gains in recoil. I personally believe that .38 Spl, 9mm Luger, .357 Sig, .40 S&W, and .45 ACP are the "best" choices for handguns for personal defense.