About any rifle round can defeat the normal soft armor worn by most police officers in the U.S. My hard armor weighs in at over sixteen pounds and won't flex even a little bit. It's level III and won't stop a rifle round going above 3,000 fps. It's a real bugger to wear. I can't imagine having to get in a foot pursuit wearing my hard vest and a duty belt. Level IV plates are a bit more durable but can be punched through with the right round. It's all about risk versus reward. Since we work in a uniform that must appear neat and professional we can't really go around wearing an external plate carrier on duty. Most patrol officers will wear a level IIIA concealable vest good for most pistol rounds and shotguns. The odds are against facing a rifle threat during regular duty. And the odds are even longer that the suspect armed with a rifle will also have proper AP ammo.
There are some rounds that are specifically designed to defeat hard armor. They generally have a hardened penetrator and travel at a velocity greater than 3,000 fps. Some Elmer Fudd styled hunting rifles can easily blow through a vest without a second thought. Those rifles can also do it at a considerable distance. Bullet design is only part of the equation.
Also, remember that a vest is just that, a vest. You are still vulnerable to a hit to the central nervous system or an extremity. It's always best to avoid getting shot at in the first place if at all possible. I will also admit that I am guilty of working in uniform at times without a vest.
Now if you're talking about shooting AP ammo at a hardened vehicle then that's a whole different level of trouble. Most armored passenger cars can easily take a hit from all but the most exotic AP small arms ammo. The kinds of protection afforded by high level government transport is even more robust. It takes more than a common small arm to take on an armored car.
The media chatter about banning AP ammo is just that, chatter. Most of them don't have a clue about body armor or what happens when a bullet hits it. Banning AP ammo doesn't really make anyone safer. It doesn't mean that officers can just go about their business safe in the knowledge that since AP ammo is illegal it can't possibly wind up in the hands of a criminal.
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