The train in NYC runs 24 hours a day 7 days a week. The London Tube stops at midnight.
The train in NYC is much much cheaper, it's $2.75 to go anywhere on its almost 400km of track. London's Tube has zone-based pricing.
The NYC subway cars are all air-conditioned.
The NYC subway cars are far roomier than the Tube.
NYCs subway is "cut and cover" and so the stations aren't nearly as deep and quicker to get in and out of.
Public transport in London is notoriously expensive though it is true.
One major failing of the NYC subway in my mind is the near total lack of signage. There is like one map per carriage (which is often hidden behind people standing or sitting), and the platforms have almost no signage or maps or directions. You look out the window to see where you are when you pull into a station and there are no signs. Perhaps there is a single letter initial every 30 meters or so... WTF? At least in London the station name is repeated all the way along the platform (along with route maps and network maps and colour-coded signs to other lines etc), there are like 8 maps in every carriage at above-head-height so you can see it over people etc.
The express routes in NYC subway are awesome and I wish London had those
I don't want to overstate this too much, I dislike the JR privatisation (including a part where a lot of the public-era debt ended up in the gov't's hand), and all the train companies here do a combo of offering the train service and doing loads of real estate offerings at each station (making them very successful organizations overall). But I believe that we would see much less train coverage without continued gov't financing in these projects.
Here is an article (from '97, granted) talking about how the gov't sets up things like interest-free loans for developing new lines. https://www.ejrcf.or.jp/jrtr/jrtr11/pdf/f14_ono.pdf
If somebody is making money off of a transaction, that money is coming from somewhere. At the margins that is fine but when we're talking about 10s of billions of dollars it just looks like a handout from the general public to people who had enough money to invest in a transportation corporation during its privatisation.
Counterfactuals are not resolvable though, but I think we can look at how this stuff was built out and decide if there are structures to do it without having to just let go of democratic control of vital infrastructure.
[0]: yes I understand that there's a universe where the public-run version just falls apart and doesn't exist.
TIL this amusing combo, thanks! The Wikipedia entry is helpful [1]