I frequent all of them quite a bit. Bistro is frustrating. They don't take reservations, and it's always crowded. The bar area is cramped. The two dining rooms across the hall are dingy. The food is ok. Better at dinner. They do a nice job with the entrees. Less so with burgers and starters. I don't think they serve booze, so wine and beer only. My one brunch there was a disaster.
Blacks is a much more sophisticated setting. The wine list is better. The menu is much broader. The service is better. The cooking is better. The take reservations and are on OpenTable. While they have had their share of issues over the years, Jeff Black recently made some changes and from what I have read and the front of the house and the back of the house are finally working together. The Seafood Stew is amazing. While they may act like they're on K Street, the shortcomings do pop up. Things like the servers not knowing the wine list. And the servers being unwilling to alter the delivery schedule of dishes. Still, you can walk away happy if you aren't too too demanding.
You didn't ask about Addies but I will chime in unsolicited. It is probably somewhere in the middle of the Bistro and Blacks. It's a kitchy decor that I don't particularly like. There is no bar to wait at. There is a big tent/awning in summer so you can enjoy eating next to Rockville Pike. And the bill is always outlandishly high for the suburban atmoshpere. And as I have said before, it seems like everytime I go all the entrees have fruit as a component.
BlackSalt down on MacArthur is by far the best of the lot. Large bar. Professional service. The best chef. The most interesting a varied menu items. A really enjoyable meal.
I haven't been to Bistro, and first knew Black's, but of the three I've been to, I agree with Pappy that BlackSalt is the clear leader in nearly all respects (food, ambiance, service).
I put Addie's as a clear second for the menu and service (we ended up having our rehearsal dinner there). Then Black's as a third - while good it's comparatively pedestrian when all lined up.
So, again, I can't say anything about Bistro.