Well, they both work and are in effect independantly of each other. Obviously, my reply is only in regards to the Nordic Passport Union. I am guessing that you are perhaps wondering, "what about citizens of Schegen countries?"

Of course, you would then be making a valid point. However, citizens of Schengen countries (when crossing the border) must still carry a valid ID, which proves their citizenship. For Danes, the only such ID is in fact the passport.