Also look into into the work of the International Wound Ballistics Association and Dr. Martin Facklers work. Also the Force Science Institute does good scientific research.
Some good info above, and expansion can play a large role in incapacitation, if it is properly designed expansion. A good explanation I've heard goes as follows:
Think of the human body as a hydraulic system. Short of an immediately disabling hit, i.e. Medula, you must cause as much 'leaking' of the hydraulic system as you can to eventually stop it. So, while expansion is important to increase the chances of hitting some organ/vessel carrying the fluid, it is the edges of that expansion that can cause the cutting of those organs/vessels in near misses. That is why so much design goes into modern bullets, such as the bullet opening into petals, with cutting edges.
Blunt edges, whether through a FMJ or poor expansion, tend to just push organs/vessels out of the way. Sharp edges cut them causing the system to leak, the more/faster the leaks, the faster the system shuts down.
Is shot placement important, absolutely, but experience shows that we as humans, generally speaking, fare poorly in shot placement when firing under stress, while target is moving and shooting back, cover used by the assaulter, etc. A properly designed bullet increases your chances of stopping the threat eventually given the average shooters performance under the worst scenario. As instructors, we always strive for accuracy and shot placement, but reality provides a different result.
The point really hit home for me after attending one of Dr. Facklers conferences. It's a demonstration I have used several times since as an instructor. You can probably find a copy of it on line somewhere. I can dig through my materials sometime to see if I can find pictures of it if someone wants it bad enough. Dr. Fackler (or colleagues at the institute) had an average shooter shoot a 9mm into a target as fast as they could. They then superimposed a clear, internal anatomically correct target over the shot target. The overlay showed organs, blood vessels, nerves, etc. You could visually see where the 9mm passed important organs/vessels. They then superimposed different caliber holes over the 9mm holes. Obviously, the larger calibers turned near misses into hits on the organs. Taking into account expansion with cutting edges, each increase in caliber increases your chances of stopping the threat if shot placement is not optimal.
Of course, you should not shoot any caliber you cannot reasonably control. I preach "One hit with a .22 is better than 6 misses with a .44 magnum."
If you absolutely have nothing else, a FMJ is better than nothing, but a properly designed hollow point is much, much better.