I don't really know much about Copenhagen but Copenhagen has a really beautiful look. The have nice architectural attractions and some really cozy cafes.
Amsterdam has a lot of places to go out and have fun. Not just hookers and weed but, fancy clubs, cafes and pubs.
Amsterdam has the Rijksmuseum. which had a huge renovation that finished last year.
I really recommend u visit this website
http://www.iamsterdam.com/
it shows you everything about Amsterdam.
If you really can't decide.
http://versus.com/en/copenhagen-vs-amsterdam
It compares both cities with each other.
I hope i could help you out with that.
Ps.
there is a indoor ski center about an hour from Amsterdam if you are interested.