Actually, an armor-piercing round would be less effective against soft tissue than a full-metal jacket because the core of the round doesn't fragment and tends to pass through. Also, not everything you shoot at will be wearing body armor, and not all body armor will defeat FMJ rifle rounds in the first place.
Oh, and a hollow-point caves in on itself when it hits armor, but will literally blow holes in you if it hits a soft part. They're much deadlier than regular ammunition.
Finally, AP rounds don't move faster. That's impossible. The only way to accomplish that in a conventional weapon like this one would be for the round to have more powder in it, which would require it to be longer, which would make it an entirely new round fired by a different weapon. AP rounds move at the same speed as FMJ rounds, but instead of being made of solid lead or whatever metal, they have a casing of lead surrounding a core made of some very strong metal like high-carbon steel or tungsten with a pointy tip.