In the art world, Artist's Proofs are generally worth more then the regular editions. With engravings, each successive pressing or print degrades the plate slightly, so the earliest prints are the closest to the artists intent. With lithographs and now digital prints, the Proofs are supposed to be inspected by the artists, and personally approved by them as "the definitive" version of that work.
Outside the art world, and especially in the collectibles world, AP seems to have little meaning. They are usually no different than any other piece made in the factory run, and may or may not have been inspected by the "artist" at all.
Like JKNO says, some collectors like APs or lower numbers, but at the end of the day, they are usually no different. On top of that, there is no guarantee that the entire edition run was ever produced. That can happen with larger items or complicated items. Than there is the whole numbering issue... where sometimes numbers are accidentally duplicated.
At the end of the day, in my opinion, edition numbers are more or less meaningless for factory produced items, save as a reference to a COA. While there is some value in them for some collectors, there is likely no functional difference.