Stephen has it absolutely correctly. Most pistol cartridges are pipsqueaks when it comes to an ethical kill.
It is generally accepted that the .41 or .44 Maggies are the starting points for serious pistol hunting--again, from the standpoint of the "clean kill".
Another aspect, regardless of the weapon used, is one's own skill. If you can't reliably hit a beer can at 75 yards, say, 8 of ten times, a whole bunch of practice is needed. With a reasonably powerful rifle, that Bad Hit can at least anchor a deer and allow a coup de grace to end the affair. A bad hit with the average self-defense pistol cartridge commonly leads to a lost, but dead, deer.
Ethics. Always ethics.
Art