I lived in Stockholm for a couple years so I've enjoyed three glorious Swedish summers and survived two dark Swedish winters. I never recommend that people make their first visit to Scandinavia in winter unless they are coming specifically for winter sports. Stockholm is a spectacularly beautiful city when the sun is shining and the water is glistening and you are walking along one of the cliffs or approaching by boat or taking in the view as you cross over the Western Bridge. It is really not quite the same when it is dark and overcast.
That being said, if you do choose Stockholm, December is a better month to visit than November. November tends to be dark, overcast, and rainy. In December, it is just as dark (it will be dark by 3pm), but there is a higher probability of snow which brightens up the city. There are lots of candles in restaurants so things can feel very cosy. There are a couple of Christmas markets (Julmarknad). Skansen has a Christmas market and special activities on the weekend and it is definitely worth a visit. There is also a small Christmas market (not terribly impressive) on Stortorget in Gamla Stan. The big department store, NK, always has great decorated Christmas windows and there will be crowds outside peering in the windows. Most of the museums have reduced hours. If you are there on December 13th (Lucia Day), there will likely be a procession and concert at Storkyrkan (the Great Church) and also at Skansen. If you want to go out on the archipelago, some of the boats will offer a "Julbord" lunch (the traditional Christmas buffet with a big assortment of herring dishes, potatoes,salmon, meatballs, etc.). You can go ice skating on the rink in Kungsträdgården. You could also take an overnight ferry to Tallinn or Helsinki, but keep in mind it will be too cold to be out on deck, too dark to see the scenery, and the restaurants and entertainment on the ferry will be scaled back.