Certainly tire casing design and tread configuration contribute to tire noise, but with the C5, the biggest contributor to tire noise is the car itself rather than the tires. The problem is that the C5 has very poor acoustic isolation in spaces behind the seats. Thus you hear the fuel pump and road noise from the rear tires and it's pretty loud. GM never addressed this problem during the car's production but did address it with the C6 which has vastly improved acoustic management in the cargo area and behind the seats.
You can try different tires with less rigid casings or less agressive tread designs and they may improve the situation somewhat but, from a road noise perspective, a C5 is never going to be as quiet inside as a C6 no matter what tire you use.
From a performance standpoint, there are few tires which are better than the F1 Supercars which were originally designed for the C5 Z. Yes, you will find tires which might be a litle quieter, but most of them will be inferior in performance. The main exception to that rule may be some versions of the Michelin Pilot line.
The Gooodyear F1 GS-D3, which I've run on my Z06, is quieter, a little better in the rain and has better treadwear characteristics, but at the handing limit, it's not quite as good a tire as the F1 Supercar. From a hardcore performance standpoint, IMO, the Firestone is a piece of junk, but they are, indeed, quieter, will be a little better in the wet and likely have better tread life.
All that said, I admit to being on the "lunatic fringe" as far as tire performance and for waxers and those who seldom, if ever run their Z06es to the limit, an alternative tire choice in the interests of noise reduction, will not be a performance downgrade in a practical sense and, given the proper choice, may improve the tire noise situation incrementally.