Your best bet would be to have a chat with Will370Z, he's had both roadsters and can advise. I believe (going on my shocking memory) the general consensus is that the 350Z handles a bit better due to wheel base but the 370Z is much more refined inside and has a few additional toys (e.g: the rev match stuff).
Personally I don't like the rear end of the 370Z roadster, it just looks too high compared to the rest of the car, hence I chose the 350Z. I'd probably go for a 370Z coupe over a 350Z coupe though.