I recommend visiting both properties during the same visit as you will get to explore and contrast the architectural and historical backgrounds of two unique homes. The estate - all 126 acres of it - is also great for a relaxing picnic on the rolling hills overlooking the Potomac River.
A bit of Woodlawn's history ... It was part of George Washington’s Mount Vernon. He gave the property to his nephew who, together with his wife, built the Georgian/Federal house designed by William Thornton, architect of the U.S. Capitol. The mansion changed owners over time until becoming a historic house museum in 1949.