On Justified, that cop with the cowboy hat can shoot the gun out of people's hands.
In real life, even if you shoot a guy center mass, if he's high, angry or just really focused, he can usually get a shot or two off before he falls or runs. My brother shot a guy in the mid-torso with a .45 - the dude spun around and jumped back over the counter and ran out the door (kept his gun in hand the whole time), managed to steal a car and drive 3 hours to miami with a bullet lodged in his spine. Got surgery there.
So yeah, IF IF IF a cop is justified to shoot, it's going to be 3-5 hollow points, center mass. And cops only carry .40 cal round here. They carry 9mm (a tad smaller) in other parts.