It is a set neck and does have a longer scale length at 25.5" which is the same as Fender Strat/Tele - certainly longer than my McCarty 594 but I think the tones are more likely to be because of the 5 pick-ups. It is a 5 pick-up model and is part of the reason its called a 509. The 09 refers the number of potential combinations and tone variations. Obviously, when in the middle selection of the 5 way, the middle pick-up is exactly the same regardless of whether you have split the neck/bridge pick up - so that's why its 9 and not '10'.
The sound is much more reminiscent of a tele/strat because these are proper 'splits' so you are using just a 'single' coil. Its the closest to a 'super-strat' too with the H-S-H set up but it can also be a S-S-S, H-S-S or S-S-H too.
Anyway, the point I was trying to illustrate is that there is a PRS that can give the quality single coil tones and, if you are after something 'closer' to the strat/tele, then look at the 509. A CU24 or McCarty 594 with coil taps aren't going to give you that but that's not a 'bad' thing either. It does give you more 'tones' to play with though and they do have their own 'voice'.
Some of Fenders tones, being bright and with more attack could come from the choice of using brighter woods like maple for the neck but a well fitted/tight bolt on neck is better than a poorly fitted set-neck with lots of glue if you want that resonance to carry through the body. I believe, like Paul does, that the quality of the guitar and its tone isn't down to just 1 thing (like the wood or the neck joint) but the combination of everything inc Nut, tuners, wood, bridge etc. I am sure the 509 was designed to give the quality single coil performance that guitarists who may prefer the super strats/strats/tele tone in the same way that the 594 was designed to give those guitarists seeking the more vintage humbucker tone with a bit more versatility with coil tapping and the quality and consistency we expect from PRS.