I own a Z06, and would prefer the Carerra GT, however, I don't have $450,000 (USA) to buy the Carerra GT. The Carerra GT has 606hp and is lighter than the Z06. Nordschleife time in the Carerra GT is 7:28, while a pre-production Z06 ran a 7:42.9, although the actual car has had slight improvements since that run.
However, the Z06 just looks like another Corvette, so it doesn't attract a lot of attention and I use it as my daily driver (or my motorcycle).
Regarding the Nordschleife "production" car record, a Radical SR8 holds the current record at 6:55. This is basically a street legal (in some countries) race car.
Sedan type race cars run faster times than 6:55, but these are true race cars with slicks. A video of a BMW M3 GTR race car running combined Nurburg F1 track and Nordschleife:
http://jeffareid.net/real/m3gtrnrd.wmv