We want to take our first trip to Spain during the last week of December 09.(6 night stay) Traveling with our boys ages 16 and 19. Can't decide which city to stay in. Our 19 year old speaks Spanish. The boys are interested more in history(military) rather than art.
Any advice?

Hard to decide, indeed.

Both cities have medieval quarters, 19th century boulevards and are full of art.

What speaks for Madrid, regarding your boys interests:

The Royal Palace is stunning.
Madrid has more than 20 museums, including some technical museums (marine museum, railway museum, aircraft museum etc.) and a bullfighting museum.

What speaks for Barcelona:

The Maritime Museum is absolutely breathtaking, with a full-size galley.

Maybe another factor to take into consideration: Hotels in Barcelona are pretty expensive, may stay cheaper in Madrid. Food and beverage is dirt cheap all over Spain.

If you have six nights consider visiting both Madrid and Barcelona. Why not? The train ride takes 2:43.

Well obviously both cities were involved with the civil war but if you are looking for swords and muskateers then Madrid is the more logical place. There is a spanish writer of this sort of thing which can make Madrid and Toledo come alive.

Bad nes Madrid will be cold in late december while Barcelona will be relatively mild

The Armory at the Royal Palace in Madrid is outstanding.
You can make day trips to Toledo or/ and Segovia.
Hard decision, but I would stay in one place for only six nights ( five days)
Barcelona is smaller, easier to navigate, brimming with history and unique architecture.
Personally, I love both cities but find Barcelona more interesting.

Have they been to Europe before? If so, go to Madrid for the military history. And be sure to go to Toledo as well. Your son will use his Spanish more probably in Madrid.( I found Catalan difficult to follow perosnally.) ON the otherhand... If they have never been to Europe, I think Barcelona is a more varied city. There is so much to do there. All the teenagers I know who have gone there loved it. As an adult, I much prefer Barcelona. Hope this helps.

Catalan is one of the languages spoken Barcelona, but I have had no problem communicating in Spanish or English.
Our Catalan friend told us she uses Spanish with her customers ( she is a pharmacist) more than Catalan.
Menus are available in both ( often all three) languages.