The Pilot Powers have a more oval shape to the tire (very noticable when the tire is not mounted on a wheel), which is why the turn in is very quick. The Corsas, Diable Corsas (and I assume Corsa III, which are replacement for the Diablo Corsa) have a near perfect cicular shape, which makes them very linear as far as turn in.
I've ridden with both types (Pilot Powers and the old Diable Corsas) both street and track and, so far, I like them both. I do have to say that the Diable Corsas are a bit softer rubber, which makes them stickier then the Powers.