You know, performance wise, the C6 is world-class. And that is in all areas, handling included. What I would do is test drive the used LS3 C6 (amazing that you found one already, btw
) and see if you can take it for a long run to see if there are any real problems like some of these people have mentioned. After that, hop in a 370Z and compare and contrast.
Like the others, buying a used sports car can be risky because you don't know what the previous owner did with it. Maybe you can pull some info on the previous owner? The reason why is maybe the previous owner was an older man or female that bought it to feel young and look cool? Who knows? At least that would give you a better perspective on how the car was possibly treated.
On the other hand, buying a new car has many benefits. You are in control of the proper break-in process, you have a fresh warranty, and heck, you have a damn hot 370Z!
Anyway, just giving my .02. Hope it helps. Good luck!