Please bear in mind that the 986(S) is 10 years older than the Spyder
So what do you need to do to have your 986S match the Spyder? Basically two things (if we disregard weight reduction and making the whole body stiffer)
a) Suspension: Install Tarret front and rear sway bars and PSS9 plus rear adjustable toe arms, that should match the Spyder's suspension then.
Total cost: $3.5k for the hardware and maybe $1.5k for the labor
b) Horsepower: You need to find 50 extra horses, and they will cost you. My rule of thumb is $100 / for each additional hp, so you're looking at at least $5k extra here
Probably the best approach would be either a TPC or Turbo Kraft turbo charger
I did all of a) and did as much of b) that I can afford (no turbo) and I passed several Spyders so far on the track. However when I meet a competent Spyder driver it looks pretty much like this:
http://www.youtube.com/watch?v=uQFSaAndK20