I've lived in both places, and they each have their pluses and minuses. The housing costs in both places are horrifically high, but they both have great public transportation. Both are places where there's always something to do, regardless of how broke you might be.
If I had to choose one, I guess it would be DC. I lived on Capitol Hill, behind the Supreme Court building, so I could walk to Union Station, or The Mall. Over a dozen Smithsonian Museums offered free admission. The food options were amazing. I could walk to the farmer's market on Saturday mornings.