ProGamer: handgun bullets do not behave like rifle bullets do. Here's an interesting report by the FBI on this issue:
Summed up: while a hit from a rifle bullet centre-mass will often incapacitate the target immediately, a handgun bullet can not be expected to do the same. Only a shot to the central nervous system is guaranteed to immediately incapacitate the target. Hits centre-mass are likely to incapacitate targets over time, but even when they hit the heart or aorta (and thus will kill the target with 100% certainty), the target may continue to function for up to 20s, until his brain runs out of oxygen.
So that's why I proposed this health system (at standard engagement range for each weapon):
Any bullet that manages to penetrate the CNS (head) should immediately kill the target.
A handgun bullet that penetrates the chest centre-mass or to the neck should drop the target anywhere (randomly) between 0-30s (to simulate differences in psychological/physical state), without ability to heal. A handgun bullet that penetrates anywhere else (limbs, shoulder, hip, stomach) should cause bleeding and performance los of said limb, but only kills if left untreated for a couple of minutes.
A rifle bullet penetrating centre mass should give immediate incapacitation and death (lung/heart/neck shot). A rifle bullet penetrating a limb should render it completely useless and start bleeding. A rifle bullet penetrating other areas (stomach) should cause incapacitation and bleeding but not immediate death.