The action-coolness of Chow probably eclipses his real talent -- the subtle detail he's able to deliver. Imagine without the well-portrayed chemistry between him and Jennifer, the movie will degrade to "just another boy-meet-girl" flick. He's the magic. Chery Chun was mostly a "vase" (albeit a pretty one :) I guess the director is the magician who delivered.
Two points to add -- (1) I believed the director herself studied in NYU (where Jennifer studied), and it is amazing how well she captured the feelings of those who study in the US from HK (typical in those days were financial stress, part time jobs, crucial peer support and cover-up of difficulties from parents). She also presented NYC in no less passion than Woody Allen (who's cited in the movie itself), except she beautified the poor-men's share and perhaps cast doubt on the rich (though with much sweetness).
(2) Most of the movie is simple and easily appreciated. But those who know Cantonese get a real bonus. In fact, Chow Yun Fat started out in TV shows, making himself cool and noticeable via his unconventional and memorable use of the language -- everything he said would be fashion for long long time (some of those terms he invented are still being used). So, the exact things he said were cute-cool-classic quotes, again, at least among the generations growing up watching him. It was unfortunate that back in those days, foreign movies were not as well publicized and received in the western world, so that his move to Hollywood was necessary for him to reach out to a wider audience. I have not seen him cast meaningfully since then :(
