Nationality is important in the sense that Hou Hsiao-hsien and Edward Yang make films about personal and national identity within their country; what it means to be Taiwanese given the turbulent history of the country (credit: All Movie Guide). Hsiao-hsien and Yang are, first and foremost, Taiwanese directors making films that interest Taiwanese people. The same is true for most directors working within their native countries. They may not be as overt as Hsiao-hsien and Yang in making films about national identity or the social & political history of their country, but they're all a part of their culture and the primary audience is their people. 

I don't think you can say Taiwanese films are better than Chinese films, and I doubt anyone here would do that, aside from saying they enjoy one more than the other. You can definitely make comparisons between the two, because it's pretty clear, to me, that a whole generation of Taiwanese and Chinese directors have informed and influenced one another, and their films contrast and complement each other. The same kind of connections could be made throughout the history of film. 

I agree with katsuben that our fascination with certain cinema usually comes from an interest in that culture (I'm personally interested in the Japanese aesthetic of Mono No Aware), but it's more useful to compare directors within that cinema (and the subject matter they deal with), or take a broader look at the history of that cinema, and where a particular director fits in. If you want to compare directors, films, or even entire cinemas from different countries, it's probably be best to compare them in terms of what's universal to all of them -- not necessarily the human truths, but the cinematic language of filmmaking and editing. 

At the end of the day, filmmaking is all about economics and where the money is, so you get producers looking all over the world for pockets of money (usually where a government has allowed a tax break for filmmaking). Thus nationality is becoming less important in modern cinema. The greater emphasis is on where the film can be shot for cheapest (even if that location is filling in for another), and cheaper distribution (provided you do post-production in their country), etc., which is great in terms of bringing the international filmmaking community together, but one can no longer say that films are entirely national, because most films that "travel", so to speak, are co-productions at some level. Most of the films that screen internationally are a result of being shown at overseas film festivals, and a hell of a lot of money is poured into getting those films screened in the first place. It's an incredibly competitive market. My producing teacher was telling us about what Cannes is like, and it's just a madhouse. 

In the end, a person's choice in cinema usually comes down to aesthetics, and those aesthetics come out of a rich tradition of filmmaking or art itself, or a turbulent political history. A lot of great films are made during or after periods of war, for instance. Personally, I'm interested in great stories from anywhere, but that in itself is an aesthetic. 