As a former DC and NYC resident who now lives in SF, I have quite a bit of experience riding the subway, Metro, and BART[0]. Here are my impressions:
The SF system is relatively nice, and regularly on time. Timed transfers are great. Shutting down so early, even on Friday and Saturday is a disaster for SF/East Bay interaction, and (on weeknights) people who work the night shift. The coverage is OK, but the fact that there's just one line on the SF side of things is a little crazy, especially given the challenge of walking long distances the hills present. Buses and MUNI are can't replace rail entirely. Finally, the variety of transit authorities makes it daunting to plan your trip or transfer services if (like a tourist might) you don't have a Clipper Card. 511 is pretty good as far as planning goes, but it'd be great to have a single map that showed BART and Muni, for example.
The DC system is far cleaner than NY, but coverage is very bad. Georgetown is devoid of Metro stops for snobby reasons, but the real desert is Northeast, which tends to be poorer and thus needs more public transit to begin with! Not being able to get to Dulles is terrible (although the silver line is nearing completion). SmarTrip works fine, but the lack of a monthly card really drove me crazy. Service is extended to 3 am on weekends, but DC is also far more walkable, and a cab ride isn't going to potentially set you back $80, even if you're in Virginia somewhere, like it would if you were trying to get across the Bay (yes, there are buses, they can get crowded to the point that they fill up and you have to wait for the next one, which can be an hour later). The Metro has peak fares, even if you are riding "the wrong way"---I commuted from DC out to College Park via the green line and paid more in the morning, even though I rode trains where everyone could find a seat. This makes no sense to me. The fare was $3.35 (the base fare of $2.65 for that trip is more than a NYC fare)---it was actually cheaper for me to drive, but the extra 40 minutes to read, do the crossword, etc., was worth the difference. If you're going to have me swipe in and swipe out and charge me based on distance, then I think you can figure out that I didn't add to the rush.
The NYC system is by far the best with respect to the problems the other two systems have, although coverage in eastern Queens and Brooklyn leave much to be desired, and Staten Island has its own set of problems, and the lack of direct airport service is a serious shortcoming. However, you can always catch a train at any time of night if you are willing to wait 20 minutes. You can buy an unlimited daily, weekly, or monthly metrocard. A fare otherwise costs a flat, time- and distance-traveled-independent $2.50. Coverage is phenomenal, in terms of the number of stations, neighborhoods serviced, express trains, and comparative resilience to service disruptions when there is construction. Finally the scale and usage are incomparable. The Lexington Avenue Line alone (ie. the 4, 5, and 6 trains) carries 1.9 million people a day[1], whereas the entire BART system carries 400,000 and DC Metro 850,000 daily[2]. My point is that the NYC subway is simply massive in a way that those other systems aren't.
I understand why NYC's system is so good: age, lack of NIMBY strength and fierce competition between different subway companies when it was first constructed, scale of the city itself, only having to deal with a single authority (now, anyway) and political jurisdiction (again, now, anyway---if the 7 ever gets extended to Hoboken, we'll see what happens). Finally, a flat fare makes sense for a city where the poor tend live far away from "important" areas (like Midtown Manhattan), and this enables logistically simpler unlimited ridership cards, whereas in DC the wealthier people tend to live in the suburbs and the poorer people in the city, so it is less regressive to charge by distance. Not sure if/how SF fits into this idea.
[0] I just noticed that the commonly used name for each of these is capitalized differently!
[1] http://en.wikipedia.org/wiki/IRT_Lexington_Avenue_Line
[2] http://en.wikipedia.org/wiki/List_of_United_States_rapid_tra...