You don't really benefit from the upgrades unless you go out of your way to fly UA as well and since they don't have a direct CPH service anymore that by it self probably isn't worth it. You get lounge access with SK at Silver which you can leverage when you fly to EWR and ORD or on your intra-EU trips.
I've never found UA's program appealing even though I fly their ARN-EWR in C a few times a year, though that will stop once SK's new interior with lie-flat is available.
Are you far away from EBG or could you qualify with a nominal push or better leveraging of promotions?