The 513, if its like a 509, does give you more of the Stratty/tele tones and you do have the SC in the middle to help. You can run it as an SSS or HSH to help get the Stratty and super-stratty type tones. Whilst the layout of the Special looks like it could be a HSH (or SSS, SSH, HSS), even though the middle in this case is a NF, its really a H,HNF,NFH,H (where H could also be Tapped of course) you do not get the Middle on its own so apart from being in Position 3 with both Humbuckers tapped, you are always paired with a Humbucker as the NF is closer to a HB than a SC.
The Special is much more a Custom 24-08 with extra options to fine tune the tone how you see fit. If the Separation between the Neck and Bridge position is too wide, you can use the Narrowfield to shorten the separation. If the bridge is a bit too bright with the neck, you can use the Narrowfield with the neck instead. It really is a double humbucker guitar but with different separation options than a regular Double Humbucker. Maybe if you could use the NF and/or if the NF sounded more Single Coil, then maybe it would be more like the 513. As it is, the Special is more a versatile double humbucker guitar which makes it very different to a 513/509
The abbreviated version is that the 513/509 is more versatile multi-instrument guitar (as it can be a LP, Stratty/tele instrument whilst the Special is more of a versatile Custom 22 with options to fine tune the 'double humbucker' tone. I love my Special but its more a Double Humbucker guitar with a lot of options to fine tune those Double Humbucker tones. Both can easily have a place without too many cross-over tones.