Well on the whole, Denmark is probably the cheapest of the Nordic countries to visit. And if you want to chill out with an ice-cold beer (which, let's face it, is one of the best things about a holiday), then Denmark wins hands down.
Walking around the streets of both cities, you will notice that Copenhagen is rough, gritty, and slightly careless whereas Stockholm is very posh and proper. The winner of this category is Copenhagen by a whisker. Its architecture and attractions are slightly more diverse.