Owned both and had a Supra TT as well. To be honest I found the Supra is as dull as dishwater, yes it was quick but it didn't feel involved in anyway shape for form to me.
The S2000 is absolutely fabulous, I loved mine and sold it only because I was relocating south and needed extra cash for a bit, I would have another tomorrow. Pro's over the Z - cheaper to run, better mpg, cheaper servicing, lovely 9.5k red line, amazing gearbox. Cons - Noisier, not much torque if you're not in the mood to boot it and can catch you out in the wet if you're not concentrating.
The 350z, is also fabulous and more refined than the S2000, in my opinion it handles nowhere near as well due to the weight, but its more civilised, the engine and gearbox beautiful. Pro's - smooth power, lots of torque, quieter, more sophisticated, more lazy. Cons - none for me but mpg is less (well its a 3.5 V6)
If I could afford both, I would have both. If you're going to track a lot it then for me, the S2000 is the car, if only doing the occasional one and you need a bit more boot room at the back then 350 just edges it.
With either motor, you'll have a great car!