What's the difference between King of Tokyo and King of New York?
King of New York is essentially King of Tokyo with some modifications:


Victory points on the dice are less dominant, having a single VP result. The other 2 faces are replaced with buildings and skulls.
There are regions and things to do for people not in the middle.
Buildings are able to be destroyed, adding a risk/reward mechanic as destroying buildings adds military units. This also adds a potential way to heal in the middle.
The skull results allow you to target people you couldn't attack if they're in a region with lots of military units.
Staying in Manhattan is more rewarding than staying in Tokyo, and the rewards grow with time.


For me, the biggest difference is how the game encourages getting in and smashing things up. In King of Tokyo, being in Tokyo was very risky and offered little reward. In my experience, the dominant strategy was staying outside and rolling for points. In King of New York, with the improved rewards for being in Manhattan, the possibility of healing or taking other rewards, and the decreased value of rolling VPs, staying in is much more viable.