The short answer is that both airports are quite inconvenient. I find the train to BWI unpractical for the reason mentioned by Often1 and a taxi will cost you $80 + or a shuttle $35. IAD is nearly as far in terms of time (less in distance), has no train, but shuttles will be a bit cheaper and a taxi will be at least around $60.

If you fly in J, it is worth noting that BWI despite being a late departure does not have the sleeper concept (lounge is ok but doesn't have proper food facilities, just a few crudites, finger sandwiches and soup) so you'll get a full dinner on board which some people like, others do not.

DCA is by far the most convenient airport for Washington but as mentioned by others requires a change somewhere and also subject to heavy delays whenever a small weather problem occurs.