If Downtown DC is your final destination, most travelers make the mistake of choosing IAD or BWI over DCA only once. Or they never use DCA and never know what they are missing.

Arriving DCA and heading downtown on the Metro vs. arriving IAD/BWI and then getting into the city is like comparing a full body massage to a colonoscopy.

EDIT to add:

IAD to the White House is 27 miles via the shortest route (Dulles Access Road to 66E into the city)
DCA to the White House is 3 miles (driving).

You do the math.