Stuff to do: NYC
We always came across more random events in New York (especially free ones). Tokyo has events, but they seem more planned and structured.
*note: we do not like sushi, so this may be a little biased.
We loved ramen and beef bowls and we LOVE eating everything with chopsticks. Tokyo has a lot of dining options, but most are Japanese and Italian. New York has way more variety, more yummy street food, and there are way more affordable options (pizza by the slice!). Also, buying groceries is easier and there's a better selection in New York.
The people are nicer and more courteous in Tokyo (not saying that New Yorkers aren't - they are - but Tokyoites are just nicer). New Yorkers seem to be more interesting. Even with Harajuku girls and traditional attire, people watching is way more entertaining in New York than in Tokyo. Overall, the varied personalities are more evident in New York.
Mass transit: Tokyo
It's cleaner, more frequent (especially on weekends), on time, and on average it's a little less expensive per ride. Your metro card can also be used in some stores as a type of debit card. It's also RFID, which is cooler than New York's swipe. The only cons are that Tokyo uses many private train lines throughout the city, and there are two different metro lines in the city (Tokyo metro and the Toei lines), and the metro card only works on one of them.
There are plenty of city workers cleaning everywhere, everything, all the time. All parts of the city, wherever you go, it's clean.
New York has made it a point to have lots of parks, everywhere. From small parks and green spaces to Central Park and Prospect Park which are massive well-designed parks with so many different areas to enjoy. Tokyo has plenty of parks, but they're not as pretty (outside of the tea gardens) and not as welcoming. You don't want to stay and relax in Tokyo parks like you do in New York parks.
Anything New York has, from 5th Ave to Soho, Tokyo has it too. And more. What's even better is that the shops here are designed well. It's so much more visually appealing to shop around in Tokyo.
Apparently Shinjuku is the most dangerous part of Tokyo, and we felt so safe there. New York is constantly getting safer, but there are still plenty of areas we don't dare go.
Cost of living: NYC
We found that it's easier to get by in New York without spending as much money. Groceries, rent, transportation, fun, it's all just a little less in the Big Apple.
On paper, it looks like the two cities tie. We could see ourselves living in either city just as easily. We love Tokyo, and possibly with time we could love it as much as we love New York. We're definitely coming back in the future. But now, thinking back on our experience, we think New York is just better.