Having had residences in the Stockholm and Copenhagen areas and having been in both places often during mid- and late-December, I prefer Stockholm to Copenhagen. Sure, Stockholm has somewhat shorter day light hours, but the chances of rain are lower there than in Copenhagen and the skies above Stockholm seem to involve more predictable weather/sun than Copenhagen.

Christmas markets in either place pale in comparison to what is to be experienced in Germany and Austria.

If you want to ice skate on natural bodies of water, Stockholm is far more likely to work out than Copenhagen; however, in December, there is little guarantee that the natural bodies of water in the Stockholm area will be frozen well enough for use. Ice skating in Stockholm in mid-December? I haven't been able to do that in a long time over the last decade because the weather tends not to cooperate for that.