Talking about New York... yes, I can see one similarity between Stockholm city (the area in the pics, around Hötorgscity) and Manhattan. The flow of people is quite even from all directions in many streets. In Göteborg it's always one street that leads the people mainly in one direction. I don't know about Copenhagen, their Ströget maybe gives that effect too. But maybe there is a center where many busy street crosses too? I hope you understand what I'm trying to say.
I like Stockholm city, ugly or not, it's busy and that's good. It gives a nice contrast to other more mellow areas in a city.
But they should try to do something about the many boring facades from the 60s, 70s. It's mystery to me that our capital has a collection of really poor architecture in the city center. Why not fill them with neon signs, that would be a step up.