I've been to both. It's difficult to compare, here, because they're different classes of cities and both have pretty different feels. Practical considerations: Price. Hamburg is much, much, much less expensive. Copenhagen slapped me with sticker shock. read more
While Hamburg tends to be a little bit more expensive than Berlin, Copenhagen is in a different league - average pricing for a beer and a meal in Berlin, Hamburg and Copenhagen are respectively 2,5 - 3 - 6 and 6 - 8 - 13 (as a very general average). read more
Because Copenhagen is on my top 10 list of favorite cities in Europe - My 10 Favorite Cities in Europe (for now) | Jagabond - then that would be my clear #1. Copenhagen is a classy, beautiful city with a multitude of castles, shopping options, and dining/nightlife opportunities. read more
In general, cities with possibility of drinking alcohol in public places have more thriving nightlife. It's easier to organize parties in public places. Source: Wikipedia, 2018; city's official website, 2018. read more