If you really enjoy the topic of CoF of wheels and tires, I would highly recommend:
Fundamentals of Vehicle Dynamics (R114) [Hardcover]
Thomas D. Gillespie
He has a lot of great documentation of test results from tire companies, and can explain some of the issues you guys are arguing over. The CoF of a rubber component on a surface is an extremely complex interaction. Contact pressure, temperature (both tire and surface), slip angle, slip ratio, and the tires ability to dissapate heat all play into this variable. These minor deltas usually are not necessary for engineering approximations where you only need to be within a few percent. However, they become a bigger deal when you are looking at performance applications.
As far as surface area effecting grip, probably within 10% (for the size differences we are discussing). Keep in mind that static versus dynamic friction can also often be on the order of 10% (or more). That means that if I had 10% more traction than you, and start pushing you and my wheels are close to the static grip level, and you are spinning yours, I may no have 20% more traction (all things being equal). This is a very frequent occurrence in FRC.
If someone did a truly down-town experiment on this, they really should document it well and enter it into a science fair. They could probably get some pretty big scholarship money.
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One of the coolest projects I have worked on in my career dealt with the %slip vs. traction and its role in a phenomenon called Power-Hop or Wheel-hop. This problem also dealt heavily with a systems vibration issue. (Vibes and Physics are often looked at as two horibly boring classes, but put the two together and you get to do burnouts in muscle cars for a few months).
