A few years ago, Conde Nast (or some other big) travel magazine did a brief write-up of several of these visit ____ [city] types of cards/passes. Some of them were a lousy value, but I don't recall if the Copenhagen card was considered a great deal or not. For Sunday or Monday travel, it may not be as good a value as it would be for other days of the week.

At least it helps avoid the problems of buying tickets for public transport when the US bank cards don't get processed smoothly.