If I understand correctly, double clutch gearboxes dont have much to do with faster gearchanges. That concerns single clutch systems. Twin clutches work by engaging two gears at the same time. For example, if you are in first gear, second gear would already be engaged so while you rev up, there's a smooth transition between the two gears. While you are in second gear, the gearbox automatically disengages first gear and engages third gear and waits until you need it.
This is how it works when it upshifts, but i dont know how it works when they downshift. Maybe they'll need triple clutches or perhaps speed doesnt matter at all when you downshift. I didnt know Ferraris ran these gearboxes in their F2002. I thought Mclaren would have been the first to introduce it in F1.
Btw, wasnt there rumors that Mclaren was developing a carbonfibre gearbox just after they signed Michael Coughlan from Arrows? I thought this would be a carbon double clutch box.