I think Chinese films are still on the very far fringes, oddities, exceptions. The most influential? Off the top of my head, I'd say Jackie Chan and Jet Li. Both for their 'brand' recognition. At least, their Western knock-off brand. To extend the metaphor, most people know and have access to their ready to wear line but not ther haute couture.
As to whether Asian films are more mainstream now, no I don't think so. Maybe Asian filmmakers are more mainstream by virtue of adapting to their environment, but no longer 'Asian', e.g., Ang Lee/The Hulk. Possibly, by sheer numbers, with more Asians in the West due to world wide emigration, it's unavoidable.
Is it good or bad? I guess it depends on whether you want to subscribe to a Unified Theory of Universal Filmmaking or prefer the Chaos Theory school of thought. ("My Butterfly Wing is more powerful than your Photon's Palm!")
As long as the 'correct' answer is not Quentit Tarantino! Else, I'll have to schedule that appointment for eyelid surgery after all.