I have a lot of experience with the car, but not as much as Chiefgroover by all accounts.
My take:
The engine is lovely. Great V6 sound, and very responsive. It suffers a bit at the higher end of the rev range though, becoming a tad asthmatic. A TT Supra will destroy one in a straight line, as you rightly say.
The chassis however is amazing. Very nicely balanced, and controllable without being harsh.
I've heard people who really know their cars talking about how the 350z will be the collector's car, whereas the 370z is for the rich boys. I haven't had a go in the 370z yet so I can't say, but I trust the opinions I've heard.
FWIW, Gunmetal 350z with Veilside teardrop exhaust and Nismo 19" Rays wheels = epic win.