Apologies, Wikipedia list km2 first for one and mi2 for the other. I still land in the middle though with Manhattan being 6 and change more dense than Copenhagen. I apologize for my haste and error.
The population density of Copenhagen is comparable to the density of Queens.
There is also a significant cultural difference. In the US, the biggest bike commuters are high school and college students. In some countries, bicycles are used by a broad swath of the public.