Here's a brief comparison between the American and Japanese versions of the film
The opening scene, set in New York, is missing from the US cut.
The title screen is different
Now it gets weird. Not only has the green tint been removed from the US version, but the scene plays maybe a second longer. The japanese version (top) ends with a freeze frame of the man in the air, the US version (below) shows the man falling down.
Remember the opening footage that was missing from the US version? A small glimpse of it suddenly finds its way back into the movie, when the assassins kill one "additional" person in their introduction scene.
The weirdest surprise comes last. While Kurata is having fun, the US version suddenly cuts and we see two total strangers dancing. Later these people (who are they anyway?) start having sex. This scene is nout found in the japanese version, quite simply because it was obviously never a part of the film. The US producers just added this scene because they thought the film needed some skin...