Honestly, you can't go wrong with either car. But the numbers tell the real story.
This is NIZMOZ's dyno. Blue line is stock and red is after his UPREV tune
Here is a dyno of the 370Z
I haven't driven a 370Z yet. And neither has NIZMOZ. So for he or I to try to compare the cars really isn't fair. But everyone who I have spoken to who has driven the 370Z has said it is clearly faster than the 350Z and is an improvement in almost every way. Heavier? I honestly don't think the weight difference is going to slow down the 370Z on the track.
Bottom line- Get the car that appeals to you the most. Either way you will have a Z Car.