The credit card market is quite different between EU and US: less sign'up bonuses, lower earning rate, less benefits overall.

For Denmark, there is not much more than the SK MasterCard and Diners. If you plan to fly with SK quite a bit (and I see you are a Eurobonus member), this could be handy. Diners is not widely accepted in EU.

If you prefer to collect point for AAdvantage accounts, you could use MR from AMEX. They do not have a "native" card in DK, however if you have an account in Euro you could use their ICC card available in DK in both Gold and Platinium. Again AMEX is not widely accepted.