[A4] My new A4 has been built! A tire mystery

[gsackerson@comcast.net]

Hi all,
  I got word from my dealer that my 2006 2.0T Quattro A4 has been built (I ordered a few options that you can only get from the factory) and is on the banana boat shipping my way. Now it's time to sell my 2002 A4. I was somewhat disheartened to see the Blue Book on that puppy - it seems that frame repair significantly reduces the Blue Book value even if the shop repairs it as good as new (which my body shop claims is possible.) But, while the value is lower than I'd like, it's still a nice payment for the shocking sticker price I'm paying for a new A4 ($38,000 with the options I selected - gulp.) I am excited indeed. I love the performance of the new 2.0T engine and the look of the front grille is growing on me.
  On another note, I'm a bit intrigued by what the lead Audi salesman told me about the difference between different size wheels/tires. My car is coming with 17 inch wheels/tires, and I was curious about what makes a 17 inch tire different than a 16 inch (or smaller.) As I understand the answer, all tires on a vehicle, whether it's a 16 inch, 17 inch or 18 inch, all measure the same from the ground to the top of the tire, otherwise, the odometer wouldn't work correctly with different size wheels/tires. Correct? OK, if I heard that right, the 2nd piece of information I heard was that the thickness of the rubber on a larger tire would be less than the thickness of a smaller tire on the same vehicle. This is where my brain starts going "huh?" As I heard it, to keep the overall height of 2 tires on the same vehicle the same, the thickness of the rubber on both tires are different to keep the overall size the same - is that correct? I guess I assumed the larger tire was also wider, but it sounds like I'm wrong on that. I always assumed that "sport" tires had a lower profile and were wider to compensate for the lower profile.
  Anyone care to elaborate or correct me on this? I realize this is probably "Tire Design 101" class stuff here, but I'm interested in more than theory - I'm truly interested to know how this translates to real world coming from a vehicle with a 16-inch wheel/tire to one with a 17-inch/wheel. Several of you already addressed the perception of the driver - that the cornering "seems" better on the larger tire even if times on a track don't prove that out. 
  Feel free to fire away!

Glenn
On the way out: 2002 1.8T A4 Quattro
On the boat heading to America: 2006 2.0T A4 Quattro