A brief observation after watching Ringo Lam's City on Fire (which has been on my to-see list for years): a film like this, and a lot of HK action cinema, naturally locates much of its action in the space of the city. American action films from the past few decades have a big tendency to locate their action in jungles, deserts, remote islands, etc (think of a number of Schwarzenegger or Stallone vehicles, or even things like American Ninja 2, if you've even seen or heard of it). Even those American films that do take place in cities (like the Die Hard series) seem more remote from the daily life of the city than that depicted in HK cinema. City of Fire has a robbery in a jewelry office that looks like a real office; when the robbers escape there are street vendors outside the financial building who flee to safety; the camera is always catching the actors moving among other people in the action scenes, whereas in Hollywood conventions the people we're meant to follow are very often foregrounded against blurry backgrounds of crowd commotion.
I don't know how well this observation would pan out if I gave it extended comparative study, but it seems to broadly break down this way.
When John Woo came to America, his films tended to be shot in open spaces and even largely in remote locations. Tsui Hark's Van Damme vehicles are both urban-centered, though, aren't they? I wonder how the two cultures/industries' spatial senses (and consequential impacts on storytelling) meshed and clashed in the big HK talent drain of the 1990s.