DCA is small, dated, and extremely convenient to the city. While it's not my favourite airport, it is Metro accessible and a 15 minute cab ride from my apartment, so I don't mind it. It also has a few airline clubs if you're a member, although those are small and dated as well.

IAD is large, dated, and (comparatively) inconvenient to the city, but it has a tonne of flights all over N. America and the globe. If I'm flying internationally or transcon, IAD is my choice.

In theory, DC does have another airport, BWI. It is dated, inconvenient (Depending on traffic, at least 45 minutes to the city, and the rental car complex is actually located in Delaware...), and infested with LCCs.

Really, though, it doesn't matter. Airports are crappy and you're only there to get somewhere else. Pick whichever one has the best fares and is most convenient to your destination.