Go for the Corvette. They don't overheat after 10 minutes of track use or "spirited" driving. (Hey, Nissan!
)
For some reason, I find the base C6 to look "plain," but the Z06 is just...WOW!
The C6 is faster by a long stretch, and I'm sure it handles well, but as mentioned, the (interior) quality just isn't there. I've never owned one, so I can't comment on reliability.
The Vette certainly has the proper makings of a good sports car, but the body just lacks that "wow" factor for me, personally. The 370Z looks like it was designed by designers, while the Vette looks like it was done on a computer. The 370Z's curves are just gorgeous. IMO, the same can't be said for the Vette.
In the end, if I had to make up my mind between a 370Z for $39,000 or a C6 Vette for $39,000, I think I would go for the Vette just because it's such an awesome discount I'd be getting.