Walkability: for pros, DC is flatter and cleaner. The Metro is cleaner and more reliable than Muni. For cons, the city itself is a bit more spread out, and its hinterlands (e.g. Tysons or Silver Spring), although accessible via public transit, are much less walkable than San Francisco's hinterlands (e.g. Berkeley or Palo Alto). But the biggest issue is that D.C. is just not really walkable in either the depths of winter or the heights of summer (although evenings can be pretty pleasant, and you can actually enjoy an evening out on a patio). Maybe I'm a wimp with low tolerances, but that's six months of the year gone right there.
Diversity: SF is around 1/3 foreign born, while DC is like 1/6 or 1/8. Almost half of SF speaks a language other than English at home, while DC is more like a quarter. DC is diverse, just not as diverse as SF.
I agree with the rest of what you said.
Metro absolutely does not serve many areas. It's a far cry from NYC or European cities, but was totally workable as long as you stuck to the city and certain suburbs.
On the nature front, there are really a lot of great public lands on the east coast. They are a bit less iconic than what you can find on the west coast, but you can still hike, camp, climb, ski and beach to your heart's content.
I think comparing SF to DC and Boston makes the most sense just due to similar size. LA and NYC are in a class of their own.