Done both. Amsterdam was cheaper - we booked Anne Frank, had lunch at the top of Adam tower and the swing, when to bodyworks exhibit, did a boat tour. It was fine.
Just come back from Copenhagen. We loved it but it is so expensive for food and drink. We got the Copenhagen card which gave us free entrance to things and also free travel. The transport system is amazing so easy. We did Segway around the city, boat tour, climbed millions of towers according to the kids, design museum, Tivoli, went to Experimentarium - quick metro ride to the suburbs, Copenhagen zoo - quick bus ride, Den Bla Planet - metro to the airport, free shuttle bus back into central Copenhagen. Christiansborg Palace. I preferred Copenhagen as there is so much more to do.
I agree that there is so much more to do in Copenhagen. Additionally, it feels a lot cleaner, greener and safer. Den Bla Planet is exceptional and Tivoli is a must. Make sure you see the famous Little Mermaid statue, the Hans Christian Anderson house and try and make it to the Open Air Museum which is a rambling museum of houses from all over Scandinavia, all fully furnished, giving visitors a chance to peer into bygone lives. It covers 86 hectares, and is to the north of the city, but only a half hour trip from the centre. The visit to the Carlsberg brewery is also highly suitable for children and they get a free soft drink included in their entry. Head to the stables to meet the brewer's cart horses and have a ride on the cart. If your youngest loves playgrounds, then KU.BE would be a hit and I think that even your 11yo would enjoy it. We also enjoyed making our way around the canals on a solar powered Go Boat, climbing the Rundetarn and exploring the free botanical garden and greenhouses.
I have been to Amsterdam but no with Kids. I have been to Copenhagen with Kids though- last Easter - and we all loved it. We had a very similar trip to l8toys by the sounds of things, and also visited the National Museum of Denmark which the dc (then 5 and 8) loved. They have a real Viking boat!
We stayed in a excellent, affordable, comfortable hotel 5 mins walk gym the station. Hotel Ansgar, I highly recommend it, and the huge breakfast buffets!
@girlundercover@BikeRunSki thank you so much! Yes houseboats (indeed most Amsterdam accommodation) is really pricey, mostly because it's such a tiny city and space is at such a premium. But it's wonderful and I'm really passionate about sharing how surprisingly fantastic it is for kids (I also blog about family stuff for the City of Amsterdam website IAmsterdam.)
Let me know if I can help with anything or answer questions (areas to stay etc). Glad the blog goes some way to convincing that it's the perfect family break!
Amsterdam is great with kids. We went last year (with a 5 & 7 yr old) and were very lucky with the weather. We ended up going to a gorgeous beach about half an hour's train ride from Amsterdam - Zandevoort I think - long and sandy.
Also da Bos forest which is about half an hour by bus from the centre. You could easily spend a day or more there. You can rent bikes (or tandems), eat yummy pancakes, go to a goat farm where you can feed baby goats, and I think they have inflatables to play on in the water during the summer.
That's aside from all the museums and stuff to do in the centre.I was really impressed by how much kid-friendly it was, having previously only gone in my misspent youth.