We'll I've just watched the online chat with Mike Cooper on Mini.co.uk.
He mentioned nothing about the Supercharger being bigger, all he said was that the blades have an abrasive coating meaning that there's a better seal->more power and a smaller pulley->more power. Looks like it's a myth that the supercharger is larger.
He also said about the cylinder head, that the inlet ports/exhaust ports are CNC machined->7bhp increase.
What's CNC machined?