I was actually curious about this earlier and had 2 guns and the mats and decided to try it out. this was comparing an armor piercing receiver against a .50 cal receiver. On a deathclaw.
Indeed the .50cal did more damage overall, even to the armored portions of the deathclaw (ie everything but the belly) but I did see a noticeable difference on the armor piercing receiver. There was less of a difference in damage output between the belly and the other parts with the armor piercing receiver. While the .50 cal's damage was reduced by nearly 2/3rds on armored portions, the armor peircing seemed to only be reduced by 1/3rd. Making for a noticeable difference.
That said, the .50 cal still did pretty much twice the damage overall, even factoring in the armor reduction. So it seems that power still beats ap, but ap isn't completely worthless if you can't afford the power.
(Note that my testing was hardly scientific. I was pretty much just seeing if it was worth hauling around an AP gun instead of just my tricked out 50 cal sniper. I may have traits that screwed the results, and I may have some natural armor pen as well)
Also the shoot through walls trait is op. not only can you shoot through walls, you can also shoot through the critter. Making weakpoints always targetable like the belly of a deathclaw, the combat inhibitor of robots, or the fusion cores of a sentry bot or power armor. Don't even need to be behind them... Sentry bots have gone from horrible death machines, to one shot fodder weaker than feral ghouls.