a few years ago standard cockers (show type) did compete with the working type cockers. The rules in Dk are that you cannot become a field trial champ unles you at least can get a 2'nd in quality on a show and you cannot become a (show) champion unless you have at least a 2'nd prize on a field trial (beginners class). And if you want to breed you still needs at least a 2'nd in quality to get your pups registrered. The owners of the working line cockers didn't like to show their cockers and decided to start their own organization with their own registration. They are no longer recognized by the Danish Kennel Club, and due to that we don't compete with working cockers anymore.
No Danish cocker has ever gained both titles (show and FT). From my knowledges only one english springer. But one of the FT champions are still able to win CQ on shows, and from what I know we might just have our first cocker double champion this year (if she takes two more wins on a FT).
I've seen both the working type and the show type work. Where the working type works fast, the show type is more slow, but more likely to find all the game.