One or two shots to a subject wearing body armor is typically enough to incapacitate them. That second shot can even be fatal, depending on the armor, the round, and the shot placement. Armor is there to prevent penetration and dissipate as much of the bullet's energy as possible. However, that first shot is going to do enough damage to leave at least a good amount (if not a ridiculous amount) of bruising around the impact zone. At that point, the body armor is compromised (not useless, but no longer fully capable). Another shot will do anything from leave a lot more bruising to fully penetrate. The most likely case is where you'll start getting ribs cracked. All subsequent shots increase the damage to the subject and each carries a rapidly increasing risk of penetration of the armor and death for the subject. Even without penetration of the armor, the human body can only handle so much kinetic energy.
In any event, it would be uncommon for an individual who's taken two shots to the chest to be combat effective. More commonly, they'd be lying on the ground in a lot of pain. Considering how many attempts it takes to get a shot on target for the head versus the center of mass, you're vastly better off going for the center of mass even if you know for a fact that your target is wearing armor. And before you bring up the North Hollywood shootout, understand that there were a number of factors that allowed those guys to carry on during the shootout, not the least of which was the poor accuracy of the firearms available to the police on scene at the range at which they were forced to engage.
It's unfortunate that the man you knew died while trying to stop a courthouse shooter. However, that one incident doesn't change the fact that the odds vastly favor center of mass targeting. Getting headshots on a paper target at a fixed distance and height, with no motion whatsoever, in an unstressful situation isn't that challenging. Getting them on a real human head at variable heights and distances, full range of motion, non-targets in the way and behind the target, in the most stressful situation you'll ever face (where millions of years of human evolution are working against you to destroy your vision, higher reasoning, etc) is one of those things best left to Delta operators who train on that day-in and day-out for years and years on end. And I'll bet if you talk to those guys, they'll also tell you that a center of mass shot is the perfect starting point as you'll get a hit faster and cut down on the motion that makes the head shot nigh impossible.