Wow...this certainly has turned out to be a pretty cool thread with a lot of great comments and observations made.
I've never had the chance to drive a C5 or a C6, but I have rode in both. My biggest complaint about both is the lack of exhaust sound. Now, I'm not saying that GM should come back with an "off road exhaust" option (AKA side exhaust), although admittedly, it would be kind of cool,

but give the car some growl.
That's one of the things I love about the ZR-1. If I may be so blunt....the car has some "vocal testicles." It not only looks aggressive, and performs aggressively, it sounds aggressive. There is no mistaking the unique sound of a ZR-1 - especially at wide open throttle. Hence my reason for not having any desire to drive my own and spoil the experience by listening to a radio.
When I first got into a C5, my first observation was that the sound was too refined; too quiet. Same with the C6 - although I have to admit, the C6 prototype I rode in did sound like it was a little more aggressive than the C5 -but hard to tell without riding in both one after the other. I've heard the C5 Z06 sounds much better - but other than a 5-10 mph "test-jaunt" over a pot-hole marked back road behind a dealership in a 2004 Z06 - I've never really experienced one.
So why are the newer Corvettes more quiet? I'm going to stick my head out on a limb and say that it's probably due to two reasons:
1. Marketing: GM's proposed customer base for the Corvette is older - with more sensitive ears.
2. European exhaust sound regulations. GM has been trying to aggressively infiltrate the European market with the Corvette. In order to do so, GM needs to manufacture Corvettes that meet European rules/regulations, laws, etc.
If #2 is a legitimate reason, then it would be nice if Corvettes built for export could have a unique exhaust system specific to European sound regulations, and Corvettes built for U.S. sales came with a more unrestrained exhaust sound. I believe Ferrari does this....BMW does this, and probably several other automotive manufacturers.
If stock Ford Mustangs off the showroom floor can sound incredibly awesome, then Corvettes should as well.
Yesterday afternoon I was shopping in a well-to-do part of Boston. As I was walking down the street, I heard the most incredible sound coming from behind. I had to turn my head back to look, and as I did, a bright red Ferrari 360 Modena was accelerating from a stop light. The Corvette should have that same effect. Before it makes it's appearance, it should make its presence known.
