We are going to Germany in the middle of September and will be spending one day in Hamburg. Is it worth it or should we spend more time in Dresden?
Depends on your interests. I visited both Hamburg and Dresden this summer. I spent two full days in each. I found Hamburg vastly more interesting than Dresden. Hamburg's Speicherstadt and Hafencity areas were fascinating, with endless opportunities for a photo enthusiast like me. Top-notch collection at the Kunsthalle. The Minuatur Wonderland is fun. Hamburg also has a vibrant 'counter-culture' scene and is very cosmopolitan. Actually, it is my favorite among the big cities in Germany.
My sole reason for going to Dresden was to visit the Gemäldegalerie Alte Meister and the Galerie Neue Meister. World-class collections, but otherwise, Dresden itself was underwhelming as a city.
"One day" isn't enough to go on. What day/time would you arrive in Hamburg, and from where... and what day/time would you need to leave to reach your next destination? And is there something specific you wish to see/do in Hamburg?
Is it worth it or should we spend more time in Dresden?
How shall anybody know without knowing your interests? In general is Hamburg of course worth visiting and different to Dresden.
I visited Hamburg a few years ago strictly to see Miniatur Wunderland. It was well worth it. So much so, that when the new sections open I'll return to see them.