What is the difference between Audi A8's turbocharged and supercharged engines?

I am trying to decide between a turbocharged and supercharged engine for my new Audi A8, but I'm not sure which one would be better for me. Can someone explain the technical differences between the two and offer some advice?

A turbocharged engine uses the otherwise-wasted exhaust gases to power a turbine, which compresses the incoming air and increases power output. On the other hand, a supercharged engine uses a belt-driven compressor to force more air into the cylinders, increasing power. For everyday driving, a turbocharged engine may be more efficient, while a supercharged engine may provide more immediate power for those who prefer a sporty drive.