Hi Glenn, I must admit that choosing between Nepal and Sikkim is tough decision. I will try to give you certain pointers to help in decision making.
In the very beginning let me tell you that both Sikkim and Nepal are amazingly picturesque that offers an unique experience in terms of culture, food, festival, etc. The time period that you have mentioned, will experience harsh to severe extreme weather conditions in Sikkim and certain routes and destination will beyond access. While Nepal being vast in terms of area covered to Sikkim there would be a lot more destination that should remain open during this period. Similar to Nepal even Sikkim will open up alternative tourist destination during this time and can thus offer uncommon experience in a positive way.
Also December being peak tourism time, Nepal will be overcrowded, while Sikkim will manage with basic demand and supply of the market.
There are several other factors to research and decide on to a spot (between these two amazing destination), however that depends on personal interest as well. Lastly, I can tell you that that both of these places are safe to travel for a tourist during December.
Hope the above helps you. Let me know if you need any additional details about these places.