The only difference that Paul himself states is that the woods are aesthetically better - at least the 'woods' that they also make the core models out of. They are all dried in exactly the same way. Of course you can get to choose different woods from the 'standard' woods used in core builds. As far as Paul is concerned, you can't hear any difference between the Wood Library/artist/private stock Maple caps - its just cosmetic.
I am not saying that there isn't differences between a PS and Core if both are made to the same specs and using the same wood combinations but according to Paul himself, these differences are no more different than two core models would be. Picking a Maple neck for example and a Swamp ash body will make a difference and as cores are all Mahogany with a maple cap and rosewood fretboard, then you will tend to hear more of a difference.
I personally believe that PS guitars, if made of the same materials and same specs, would sound very similar to a core with the differences you would expect from any guitars in the same model. Until I can be proven wrong, then I have no reason to believe any different. The woods are cured in the same way, the instruments still go through the same build with the same methods employed. I can't see the 'Eagle' on the headstock making a significant difference to the signature. I think a lot of the differences are related to wood choice (being made of different woods to the core models) and/or the price difference having a placebo effect (if they are finished in the same way - not nitro for example).
The only way I think this can be proven one way or another is by having a selection of core and PS models, all made using the same woods and in a blind test compared for both tonal and playability. If they are built with the same variety of woods, same neck shape, same PU's and Switches, same type of finish, then I really don't think you could literally feel any difference in a blind test and I would be very interested to know if anyone could pick out the PS amongst the cores either. If you had say 5 people in a room all blindfolded, 1 PS with 4 core models, taking it turns to play a guitar (so you start with 1 guitar and pass it round each person before moving to the second), without discussing as a group so can't influence any one, I bet they couldn't pick out the PS. Not only after hearing it played by 4 different people, but also after playing it themselves, I am willing to bet that they wouldn't be able to tell which guitar was the Private Stock. If ALL 5 independently pick out the PS, then I would believe there is a discernable and clear difference. 1 or 2 could be just a lucky guess but all 5 would be proof - especially if they can give a 'clear' reason why - whether its clearly audibly different and/or feel different.
I can't see how, if the woods are all cured the same way, separated off for purely aesthetic reasons, built in the same way albeit by different people but still glued up, CNC'd to the same shapes, using the same hardware/electronics etc that there can be a 'noticeable' difference in tone/feel in a 'blind' test so you can't see the eagle on the headstock for example. Obviously I can see the aesthetic difference, even understand how different wood variety, finish type etc can change the tonality noticeably, even understand how the price, aesthetics etc can influence people like a placebo effect.
If Paul also wants to send me a Private Stock to change my belief and opinion, I am more than happy to receive one...
