I can tell you the following:
1) They are not supervised by an organization (e.g., the vaad of this or that), but by an individual rabbi, Rabbi Hecht. You can find him onsite whenever the store is open.
2) One shabbos, probably 5-7 years ago, the Rabbi of my shul, which is in the neighborhood, mentioned that he doesn't recommend Pic-N-Pay. He didn't say why at the time. Later, I was told by friends that they asked the Rabbi for details and were told that there were a few issues, among them that the owners weren't shomer shabbat (even if the store was) and that Rabbi Hecht didn't have the only key to the lock on the freezer. My friends also said that Rabbi Hecht and/or the store-owners claimed that the shul rabbi never contacted them to discuss these allegations. None of this made me happy, since I had been doing 90% of my meat shopping at Pic-N-Pay until that point (they were about 20% less expensive for meat that Glatt Mart down the block, with comparable quality), but the bottom line is: ya gotta listen to your Rabbi, so I did. I now buy 90% of my meat at Glatt Mart. And while Glatt Mart leaves much to be desired -- high prices, erratic selection, and some surly employees (especially the blond woman, but not only her), at least I don't have to deal with Bruce (one of the owners at Pic-N-Pay), who was verrrrrrrry unpleasant himself.
So my bottom line is: Ask your Rabbi what he thinks.