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Based on the 2017 program, having an armband will get you access to things like "luxury toilets" (LUKSUSTOILETTER), the Royal Distortion main stage, and free beer from 16:00 - 18:00 at Country House (RΓ DHUSPLADSEN). I can't tell if it will get you into the street parties or not.
Here's a link to the 2017 program (PDF).
There's a statement in the program, that you have to trade your online ticket/receipt for a wristband on-site and that you cannot buy tickets at those locations.
If you look at the last page of the program, it says that the arm band gets "street benefits" (so do the other tickets).