If you go to the manufacturer's page of the two models, you will notice that the BEH2 supports 2 internal drives, the BEK only 1. This is probably why the BEH2 case is higher. But I can't explain the price difference either.
The power supply is heavy and is a bit (~5mm) longer than the NUC case (~130mm) and about 50x30mm in profile. It looks like the typical laptop power supplies.