First and foremost, federal law prohibits armor-piercing handgun ammunition for non-LEO's. Armor-piercing ammunition is specifically defined by bullet construction and material by law. Secondly, armor which incorporates hard trauma plates will stop all common handgun cartridges regardless of bullet construction and material (NIJ level IV body armor is rated up to and including 30-06 AP ammunition).
With that said, you have to understand how body armor works in order to understand which cartridges can defeat it and why. Body armor works by distributing the force of an impacting bullet over the largest possible area thus preventing its penetration. Because of this, a bullet which imparts the most force on the smallest possible area will be most likely to penetrate the armor. The most effective cartridges at penetrating body armor are those which drive a small-diameter, non-expanding bullet at high velocity. The two most prominent examples of such cartridges are 5.7x28 FN and 7.62x25 Tokarev. If a very light, non-expanding bullet were used in a long barrel to get the highest possible velocity, a handloader might be able to work up a loading in .357 Sig, 9x25 Dillon, .357 Magnum, .357 Maximum, or .327 Federal Magnum that could potentially penetrate NIJ level II armor.
The tradeoff is that the very attributes which make a bullet effective against armor also make it rather ineffective against unarmored people. The loadings which I described above would, in soft tissue, create very small diameter "icepick" wounds that would most likely go completely through a person with relatively little tissue damage. Because of this, most people who carry a handgun for defensive purposes, including police, choose a larger diameter bullet and/or an expanding bullet. This choice is made because, while inferior against armor, unarmored attackers are far more common and thus more prudent to be best prepared against.
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