New Yorker and a straphanger for decades here. Commenting on the "{City} subway system is clean. Why not NYC's?". The subway is cheap, and runs 24 hours a day. This limits how much one can clean it - Washington DC subway system washes all its platforms with hot water and bleach every night, when the subway system is closed. I believe it is a combination of non-stop, utilitarian and ancient system that brings bad rap to NYC subway. I personally favor it over cabs for a reliable, cheap ride.
They also wash the platforms with water and bleach in NYC, while people are waiting for the train.
The times I've watched it, they do an incredibly lazy job, so the net result is not much cleaning. If the goal was "clean the platform" instead of "look like you're cleaning the platform", the system would probably be a lot cleaner.
The MTA has a large number of labor relations problems they need to fix. That's what's really holding them back.
(I also watched an interesting exchange recently. Someone jumps the turnstile. Someone reports that to the station agent, who just watched it happen. She replies "are you sure, I didn't see that", and went back to playing with her phone. This attitude of neglect completely kills the "if you see something, say something" culture the MTA tries to instill. If I see something, I'll keep it to myself to avoid the ridicule I'd receive from the employees or police.)
NYC is also by far the largest and most complex subway system. The larger stations are built as underground, multilayered labyrinths. Times Square/Port Authority Bus Terminal is probably the worst offender -- it's two stations linked by an underground tunnel that services most of the subway lines in Manhattan (1/2/3, A/C/E, N/Q/R, 7, and the crosstown shuttle). Walking from the shuttle platform to the bus terminal feels like you're walking half a mile, and you go up and down several staircases and make several turns in the process.