Stopping power is not really fully understood, but the best approximation useful for comparing different cartridges is to estimate the amount of light that a wound lets in to the body. Larger calibers let more light in, therefore result in more stopping power. Same for wadcutters and expanded hollowpoint bullets. Letting in light from both sides of the body can almost double the stopping power, particularly if the diameter and shape of the bullet is already adequate, thus one can see that penetration is important. This is usually a function of sectional density and velocity, but the bottom line, as before, is "How much light does the bullet let in?" Needless to say, this basis for comparison holds true only when shot placement is held equal. It is much more effective to shed light on the CNS, or even the heart, than to illuminate the buttocks (at least from behind or beside; lighting up the buttocks from the front may actually do a pretty good job of putting a person on the ground, which makes it much easier to shoot him until he lets go of his weapon).
For reasons that are not yet fully understood, a cartridge that is adequate in daylight is usually adequate at night, even though the actual ambient light is often limited.
Hope this clears things up a little.