Personally I reckon the difference between the F1 and Veyron can be summed up like this:
GM set out to create the ultimate sportscar whereas Bugatti plan to create the ultimate supercar.
The debating about what constitutes a supercar on here is kind of ironic since GM has never used the word when describing the F1. He hated the word for all the negative associations with it.
A sportscar according to GM should be light in mass and controls, have a bit of roll to let you feel what the car is doing in corners and have a generous and responsive engine. It should be packaged well and have racecar DNA without being a roadgoing version of one.
A supercar on the other hand must be ludicrously powerful, tremendously exclusive (by being incredibly difficult to get hold of and be extraordinarily expensive once you have) and so exotically beautiful that it snaps knicker elastic at 100 paces.
Of course sportscars are ordinarily designed to a cost. The F1 shows what can happen if you don't...