Copenhagen or Stockholm

If you mean "base" city as a place to make daytrips from... neither is really suited for that purpose, but I might give a slight nod to Copenhagen over Stockholm. Some of the most interesting historic sites (like castles) in Sweden are far to the south of Stockholm, and the most interesting natural areas are far to the north and west. Stockholm is a beautiful city, but the surrounding area isn't the most exciting in Europe. The area surrounding Copenhagen is a little more interesting than Stockholm, plus you have easier access to southern Sweden. Just keep distances in mind. Scandinavia is HUGE (if you pivoted Sweden southward on Malmö, the northern extremes of the country would reach nearly to Sicily), sparsely populated , and transportation links between and within the countries are not as rapid as some other areas of Europe.

I agree with Tom in that Copenhagen probably has better day trip opportunities. Either city is remote from Norway and so will take a ferry or flight to get to. Both cities are fantastic and it's hard to recommend one or the other. It comes down to personal taste. Stockholm does offer overnight ferries to Helsinki and/or Tallinn, which includes amazing scenery of the archipelago.

I think there is more to do in and around Copenhagen than Stockholm. Stockholm has a good ferry "triangle" option to Helsinki and Tallinn that's worthwhile. You might check out cruise options to see some of the Capitals in the area like this: http://www.vacationstogo.com/fastdeal.cfm?deal=32731 Food and lodging are expensive in the area (as are ferries) so a cruise can be relative bargain. If your flights are open jaw, you could also board a cruise/ferry in Copenhagen and end in Stockholm, or vice-versa - spending a little extra time at each end. As you can see by the link, I like vacationstogo.com because of their great search engine. I've booked several times through them, including a Baltic cruise, and have never had a problem. Their prices are as good or better than everyone else.