This matchup features a city that built cars, which just might end up influencing some of these scores. The other city was built to a plan before the car was invented; perhaps that may matter too. Here's Detroit (where my grandparents lived for most of their lives) vs DC (a metro with multiple relatives and the best man at my wedding).
Category 1: Visiting Without A Car
a) How can you get to the city?
The train and bus to Detroit from, say, Chicago, are not bad at all! There is even cross-border bus service to Windsor, ON, though it's stopping on September 1. You can get a bus from the airport to the city also.
Washington, DC is the bottom of the Acela corridor on Amtrak, has multiple other train destinations and robust intercity bus service, a regional rail link to Baltimore, and three airports all accessible via rail (2 on the subway, BWI-Thurgood Marshall via regional rail).
Detroit is served by multiple very fast interstates, but that's kind of the opposite of the point here.
VERDICT: Detroit 0, DC 1
b) How do you get around?
The Detroit People Mover is notoriously pointless. There is a newish electric tram along Woodward Avenue, and it's doing pretty well. Continued attempts to get real mass transit for the region have not yet come to fruition. In the meantime, you're gonna be using a car to get around most of Detroit, especially the metro area.
WMATA has flaws, as all US transit systems do, but is largely considered one of the biggest successes in the post-war metro building boom in the US. And to add to that, most of downtown DC is eminently walkable: the National Mall famously so.
Also pretty bikeable, come to that.
VERDICT: Detroit 0, DC 2
c) What are the limits on a visitor without a car?
In Detroit, it's the giant caverns torn through the metro area by the interstates, and also the lingering effect of urban blight/renewal cycles that means places you might want to go aren't necessarily close by each other.
In DC, it's that the public transit might be slow, or you might want to go to one of the regional Smithsonian locations that are out in Virginia away from transit.
VERDICT: Detroit 0, DC 3
Category 2: Living Without A Car
a) Can you expect to get to work?
Detroit built its commuting culture and thus infrastructure around the car, because Detroit is a center of automotive industry, or at least was. About 6% of Detroiters use transit to get to work, according to the census.
DC has one of the largest commuter shares by transit in the country, about six times larger than Detroit's.
VERDICT: Detroit 0, DC 4
b) Can you live the rest of your life?
Detroit and DC have opposite issues here: DC is expensive, Detroit lacks accessible basics like grocery stores you don't have to drive to. These are both big challenges, but since the question is largely focused on whether you can do things without a car (which reduces costs) DC becomes the winner here--just by less than some of these categories.
VERDICT: Detroit 0, DC 5
c) How are the basic amenities?
Detroit gets a bad rap for this sometimes. There are lovely parks, and the art museum is world class. But DC's parks and museums are literally second to none in the US, and frankly I've walked too many places with bad or missing sidewalks and crossings in the Detroit metro area to give this the tie.
Sorry, Detroit! You aren't bad at this, but DC is excellent.
VERDICT: Detroit 0, DC 6
Category 3: Miscellaneous
a) Are there people on the street?
Look, there aren't always people on the street in DC:
But there are most of the time. And while Detroit also has more eyes on the street than you might imagine, it's still not close.
VERDICT: Detroit 0, DC 7
b) Where is the city's urbanism going?
Detroit's transit probably has a better chance of future funding for expansion: DC is at the mercy of the federal government and local governments that are also dependent on the fed, which is not a blueprint for success. WMATA has spent some time under threat now, in fact.
Of course, DC will remain a denser and more interconnected area, but the trajectory is potentially one of the few advantages of Detroit.
VERDICT: Detroit 1, DC 7
c) Is it functionally diverse?
Both of these cities are fairly diverse by US standards; both of these cities have historical legacies of discriminatory zoning and housing. DC is actually majority minority; so is Detroit (78% Black!) but the metro area is not, making it by one calculation the most segregated city in the US.
VERDICT: Detroit 1, DC 8
d) How do people there react to knowing you're not using a car?
This one is easy. Detroiters will boggle; DC will consider it pretty normal.
VERDICT: Detroit 1, DC 9
e) How do people react to people living close together?
Detroit does not have a fundamental problem with this, but DC is much denser (about twice as dense).
To be sure, there are places that are less dense in the DC Metro, like at the end of this Metro line, but even there that's a park--there's plenty of density in the other direction.
FINAL VERDICT: Detroit 1, DC 10