It isn't what Scorsese added to this movie so much as what he took away; it's shot-for-shot what got him that Oscar. I wish I'd seen this first. Tony Leung doesn't really get dirty here, and mostly just saunters around looking for trouble, sometimes finding Andy Lau (but not Maggie Cheung). The director/cinematographer Andrew Lau does a solid job in downtown Kowloon but unfortunately decided to milk a sequel and another which I now have to watch. Lau and Leung are back for the third.
Rated #228 in IMDB's top-250.