On the other hand, the NYC system is not particularly dirty. I'm not from NYC and so haven't ridden the subway a lot, but I've never seen a single seat unusable because of filth. That shiny plastic stays pretty clean.

I think the DC subway system is cleaner than the NYC subway system, but I don't think it has anything to do with the food policies. For one, I have never seen food refuse in the NYC subway. I think the biggest difference is scale and number of riders: the DC metro has about 700,000 riders on a weekday, while the NYC subway has about 5.1 million. (From Wikipedia.)