If you’re comparing center cities, I’d say that SF might trump Manhattan right now. For sure SF would “win” over the five boroughs of NYC.
I’d also say that my gut says that SF + burbs is more expensive than NYC + burbs. There are a lot more poor/cheap areas within 20 miles of NYC than near SF.
Keep in mind also that this survey totals average costs. It doesn’t compare apples to apples. If the norm is a 4 bedroom house in city #1, and people spend slightly more on housing than in city #2, where the norm is a 2 bedroom apartment, city #1 will be seen as more expensive. Even though you actually get more “bang for the buck” in city #1 and could live more cheaply (take roommates, buy a duplex, whatever).