By default I would sit on the West side - since the morning sun can be kind of harsh. Somehow - the afternoon sun is not as bad - as the morning sun is on the East.
Although the Potomac river will be on the left. I think the scenery is fabulous from Washington, DC South. I really like the Potomac, Fredricksburg, VA, Ashland, VA (nice), The Viaduct in Richmond over the James River (Grand view), Southside Virginia (farms, farmland), Eastern NC (nice), South Carolina swamps.
I think it is a very scenic route - just no mountains. But I love rural landscapes. Plenty of aesthetic farm settings, and small Carolina towns.