I am somewhat cross-eyed; when I looked at the 370Z, it looked like a Porsche!
You remind me of kids buying the latest, greatest, biggest sports-bike. They think they can smoke anyone with a smaller, older model. However, they do not understand that the 'tool' is only as good as the operator. I bet that if you owned a 370, you could smoke a comparable, stock 350. Or, simply put, if you could clone yourself, and your clone will drive the 370, he would smoke you.
If you smoked a 370Z, more power to you. Your 350 is perhaps faster, and if it is, just be happy and proud of it.