Once people have enough money to buy a car, they will. And when there are enough such people, traffic congestion will be pretty awful -- even when there is substantial public transit. (This is so unless roads are properly priced.) Moscow's pride-of-Stalin subway is only second in the world to Tokyo's in terms of passenger volume. And this was useful in impoverished Soviet days. But a measure of prosperity ended that. Details in this week's New Yorker (abstract here; rest is gated).
But the modern Moscow touch makes a bad situation much worse. The rules of the road are missing. Both law enforcement and driver etiquette leave much to be desired. Awful (or no) rules trump a great subway.
How about Beijing? H/T Craig Newmark