The nice thing about the train is that when you get off, you are in the middle of the city. From any of the airports you have an expensive cab ride in town.
I always take Acela first class, very roomy, great service, etc. Although it will be about the same price as your $179 plane ticket, you will not need to go through security, arrive an hour before your flight, shlep through the airport to the cab stand, or take the cab from one of the DC airports to the city. I travel that corridor frequently. Get off the train and the cabs are right there.

Love the Four Seaons. The Ritz Carlton (Foggy Bottom) is ok but would pick the Four Seasons first. Have not tried the Mandarin yet but sounds like I will have to.