Pros: Great furnishings (fridge, appliances, instant boiling water out of the tap), and location (Nørreport station is central to basically everywhere in the city). Also, just space to stretch out compared to a hotel room.
Cons: It's up three flights of stairs (and there's no elevator), which can be tiresome when hauling loot and a two-year-old up to bed. The second bedroom has windows which face the street, which would be fine if not for the bar on the street, which can get noisy at night.
tl;dr: If you want to visit Copenhagen with your family or friends, Jesper's flat is the way to do it for sure. You will be pleased.