Yes, I have a PS509 and a PS513 with practically the same wood. Both are maple necked monsters with slightly different fretboard woods, Brazzy vs. Kingwood. And, both of them are hand-wired though the 513 PS's is a little more creative than the average 513.
When you ask about how they compare, it becomes a loaded subject. I still love both of them for different reasons, but the fact that the 509 has replaced the 513 for the time being is a sore spot for many. The truth is that they are different instruments that only look similar. Yes, they both have a similar strat like coo on the neck pick up and a similar brightness. But, there is a definite difference in the pick ups as the 509 is clearly more articulate with more rounded highs. The voicings of the singlecoils are also closer to strat territory on the neck and tele on the bridge, and it twangs a bit. And, there is no drop in volume between single coil and humbucking modes that one would see on a 513, because the 509 is actually hybrid of a 408 and a 513. So, it's coil stealing like a 408. BUT and this is a big but, gone are the modern humbucking tones that 513 people love-- that semi-muddy, almost untameable thick goodness. The 509's humbucker tones are closer to the clear humbucking mode in the 513 and even that has more of a vintage flavor. I am not really a fan of the pattern regular neck on the 509 and still would prefer that PRS went back to the original 513 carve neck which was slightly narrower and deeper than a pattern neck, but that feature and the modern bird inlays that made the 513 more unique vanished with the 25th Anniversary 513.
I suspect that the 509 production models are bit different. They'll be less bright with more harmonic bloom than the PS which is a characteristic of a mahogany neck, but I suspect they still have the characteristic rounded highs. They'll also have less sustain and might sound a touch thinner due to the fact that the Gen III trem doesn't have the locking saddles that are on the PS. That's not a bad thing necessarily, because the locking saddles make it a little bit of a pain to change strings and are not captive which makes them likely to go missing at some point.
Then, there is hand-wired vs. not hand-wired. The 509's all are, and some of the 513's are. The PC board in the 513 that was used to streamline electronics assembly makes it less open sounding especially the oldest ones. If I recall correctly, the last couple of 513's off the line were hand-wired.