Having lived only in DC and SF bay area, I find HOV lanes to be much faster relative to traffic in DC. The data is less reliable, but I also observed HOV cheating to be much more common in CA, and enforcement to be stronger in DC.
There aren't any HOV lanes actually in DC that I know of.
395 and 66 are two interstates that connect DC to the Virginia suburbs. The HOV lanes on 395 are usually more open and faster than the main highway. 66 is entirely HOV inside the Beltway during rush hour, so if you want to go that way at all, you need passengers.
Virginia just added HOT (passengers or pay) lanes on the Beltway itself; these are usually very clear because you need a transponder to even travel within them legally, and most people haven't bothered to get one. Maybe because the Beltway doesn't actually go into the city, so the utility is low for rush hour.
There isn't enough highway in DC to make express lanes worthwhile.
The benefit of HOV on 395 & 66 comes from having limited access. The lanes get crowded during rush hour, but they still move faster because of less merging & exiting. When traffic is all moving in the same direction at the same speed it flows smoother.
The changes to the Springfield interchange did a lot to prevent backups by reducing the amount of lane changing necessary to get on and off the Beltway.