I'll chime in here since I've had all three.
C5Z: Quick, nimble, pulls very hard at the top end. Has more road feel and is more of a driver's car. The ride is firm, especially if you lower them as I do. There's not much I can complain about on this car. It's wonderful.
C6: Mine was an 05 Z51 6M. I bought this as an interim car as I knew the C6Z would not be released as an 05 car. I was amazed at how this car rode. It was so quiet and refined. This is an attribute that many C5Z owners do not prefer. However, I loved it. Low end performance with the Z51 6M was amazing. The LS2 mated to the Z06 ratio tranny, added to a little more torque and it made the car feel much stronger on the bottom end. However, since the car was outfitted with the cam profile from the 01Z instead of the 02 and up Z, it ran out of power at the big end. I'd summarize with quiet, refined and I loved that car.
C6Z: Wow! This is the know all, see all car. I speculated what this car would be like from day one of the crazy posts on the internet. Therefore, by the time the car came out, I had very high expectations. This car has met and exceeded every one of them. Power is awesome from just off idle to the red line. It just keeps pulling and pulling. I'd say the ride is a little softer than my two C5Z's. Steering is precise and the car just handles well. This car is amazing.
I hope that helped.
PS. My current two Corvettes are my C6Z and a Twin Turbo 402 Stroker C5Z.
The C6Z dyno'd at 483 RWHP with only a tune and no filter. The TT car hasn't been dyno'd yet.