Why are you comparing the SF bay area to the city limits of New York? Better would be to compare SF bay area to New York Metro Area, which is far bigger than the SF bay area.
In other words, some people tend to think of NYC as "huge major East Coast city" and SF as "huge major West Coast city", but the sheer enormous density of NYC makes it actually on a whole other level than SF.
Chicago's urban population is 8.66m, and the urban area is 2,200 sq miles. I feel like I'm in a city here. When I go to West Coast cities I feel like I'm in a giant (sometimes quaint and charming) suburb. There's no density.