Just one point about the weather affecting the racing - I seem to remember in the early days of the Bridgestone/Michelin battle it was essentially decided by the weather as the Michelins ran better in cooler conditions (and Michelin had very few sets of intermediate tyres which made wet races slightly easier for their opponents) with the Bridgestones more dominant in warmer ones.
There were other subtle differences Tom, but you're essentially correct. Michelin tended to prefer a softer tyre wall. This increased the tendency to flex when cornering, which also generates heat. The Bridgestones (essentially designed by Schumacher, for himself) were stiffer, but less prone to overheating, especially in warmer conditions. Extra side-wall stiffness requires a subtle softening of suspension components (this is relative to the softer tyre walls of course –which I say because Schumacher tends to run a very stiffly sprung car, in any case). The result is that ride height is more predictable and more consistent for the duration of a race. This in turn, was given significant extra help during the refuelling era when a car's weight was far less variable than now; it being much lighter for twice as long. Furthermore, the minimum chassis weight was also lighter than today's! The logic is simple: in warmer conditions, Schumacher, Bridgestone and Ferrari had a win-win-win situation; and that before even considering the opposition with no other front running team on Schmucks (oops, I mean Bridgestones). Oh, speaking of opposition, I should mention that this did not include a team mate either! I'd better stop before talking about the FIA…