Street noise isn't really an issue for me. The windows are double-pane with a thick space between the panes, and in my particular case the apartment isn't on a street with much automobile traffic anyway. Unlike an NYC-style grid where every street is a major street, Copenhagen has a lot of "neighborhood" streets that are deliberately designed to be hard for cars to use as through streets (chicanes, changes of one-way direction, etc).

The bigger noise problem in older buildings (this one's from 1910) is internal noise; they're not very well isolated between floors and units. Newer buildings are better for that.