Population density stats are often negatively correlated with CBD built density. The least dense neighborhood in Manhattan is around Wall Street. Midtown is the second least dense neighborhood. Similarly, I'm not sure if Center City's lower population density says much about its built density relative to downtown SF.
In any case, IMO it's hard to argue that Center City Philly, south of Market Street, and especially around Rittenhouse Square, doesn't have extremely strong similarities to NYC. It's definitely the closest street level feel. Walnut Street and Chestnut Street are likely the best examples.
https://www.google.com/maps/@39.9500432,...6thumbfov%3D100!7i16384!8i8192?entry=ttu
The interplay of skinny prewar midrises and the leftover taxpayer lots is pretty unique to NYC and a few blocks of Philly, and maybe a bit of Boston. It's a very textured feel. Walnut and Chestnut give me downtown Brooklyn vibes, or maybe a scaled down Flatiron-area avenue, around Union Square or Madison Square.