How they compare to CAC. Important? For a double eagle how much more should it add to the purchase price? (Approximately tens of dollars or hundreds of dollars)?
We are all capable of making and applying PQ stickers to coins. These are intended to draw a buyer's attention to such coins over coins not so labeled. Ultimately, the premium carried by such a designation is only what the buyer and seller mutually agree upon. In fact, if a substandard coin is so labeled, the premium should be considered negative, bringing the final price down from that of a generic coin of that date and grade.
Are you talking about these? http://pqapproved.com/why-pq/ I don't think anybody gives them any weight beyond someone writing "PQ!" on a regular sticker and sticking it on the slab. I personally give them no weight. Even CAC stickers don't carry a lot of weight for me... I just use the grade on the slab as a starting point, see if I agree with the grade, then decide if I want to pay the money being asked.
@jaceravone is an authorized PQ dealer, in addition to being a CAC dealer. He can tell you more about them.
Personally, I have NEVER seen a PQ stickered coin that I disagreed with. I can't say the same for CAC.