APR has a GT25 kit available for the Beetle.
http://www.goapr.com

4-Motion and Quattro are just marketing names. They dont refer to a specific AWD system.

The A platform cars use Haldex which is a hydraulic clutch based system. Haldex cars are FWD biased.
http://www.haldex-traction.com/

The B platform cars and all other Audis use TorSen differentials which is a series of worm gears.
http://www.torsen.com/