I have been to Amsterdam on two occasions for a weekend break and I've spent one day walking around in Copenhagen.

When you say a family, what age are your children?

Amsterdam does have the excellent NEMO science museum which is great for adults and kids but is mostly art museums, restaurants and theatres. there is also the Anne Frank house which is a must. Oh and not forgetting bike hire, boat rides though the canals and of course the trams are a fun way of getting around. there is no getting away from the fact that Amsterdam does attract stag parties and can have a rather lively nightlife.

Copenhagen is a beautiful city with many impressive historic areas and some very pleasant parks. I really enjoyed spending the day walking around the city. The harbour area is especially nice and of course there is the little mermaid connection.

Normally I wouldn't recommend Amsterdam for families but as it's only for a couple of days either city would be more than suitable. I suppose it mostly comes down to what you want to do. I think the NEMO science musieum, Anne frank and Van Gogh would swing it for me.