The Londonist recently published a series of infographics comparing the subway systems of the two cities on multiple fronts including price, distance covered, cleanliness, ease of navigation etc…
Even with the inherent bias, they called the matchup a draw.
In short: the London Underground is easier to navigate, the New York City Subway has bigger, actual air-conditioned cars. The stations are cleaner in London, New York is cheaper. The staff are so much nicer in London, you don’t have to travel to the centre of the Earth to get to a train in New York. The space issue counts for a lot, it’s not just one tick in a box for New York. Yes, London has an older network, it covers a bigger area, but New York has more stations, more lines (technically speaking) and carries more people each year. London is way more expensive, but New York does run 24 hours a day. Many will disagree, but we’re calling it… a draw.
Instead of determining how well a system works for tourists and rookies, it’s probably best to compare how well it works for locals. Given that, I would say NYC has London beat hands down.