There are a few facts that are helpful here.

To attend a HD program in Denmark or the Faroe Islands, you need a gymnasium or equivalent degree.

A HD program takes two years to complete full-time (four years part-time)

To attend any given Associates program in America, you need a high school degree or its equivalent.

An Associates program takes two years to complete full-time.

While there are many Jurists, CEOs, business professionals and so on who take a HD degree, it does not equate a graduate degree in business. My conclusion is, HD is the equivalent of a business administration degree with the same period of study, an associates.

HD consists of two parts, and the first part is called the Graduate Certificate (in Aarhus at least).

Assuming that most students go on to take the full four-year course, they would end up with a Graduate Diploma.

http://executive.au.dk/en/hd/

http://econ.au.dk/education/graduate-diploma/

A Master´s degree takes five years. (In Economics it would be called cand. oecon in Aarhus).

Although the other universities´ programmes might be slightly different, and there are several different subject choices - administration, marketing, accounting, and so on.
However, I think you would find the levels were comparable at all universities offering HD programmes.

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Note added at 20 hrs (2013-01-27 19:50:21 GMT)
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The two and four-year HD courses are part time.
Cand. oecon and all cand. degrees are full-time courses, naturally.