I caught this piece on the Guardian recently, and thought it was interesting, since the Economist has been discussing something similar lately (and indeed, it talks about a book by two Economist bigwigs - that's what I get for linking to something without rereading it!). I have, in fact, had arguments about this subject with friends from time to time, although the word I used was "democracy" rather than "Western model".
I'm a proud democrat (and sometimes less proud Democrat), so I feel it's worth repeating that "triumphalistic" or "teleological" interpretations of history, in which we're promised that if we all just adhere to Western ways of living, don't sum up my own view of history, or really that of most people. Francis Fukuyama may have proclaimed the end of history after the Soviet Union collapsed, but I feel like the only people who took that seriously were those who've never read any history themselves.
You could even say that democracy (Western-style or otherwise) has been suffering ebbs and flows ever since the end of World War II - you only have to look at the history of places like Indonesia or the wider Arab world to see that the process frequently gets hijacked. That doesn't mean, to my mind, that you ignore the whole concept of personal liberty.
But I do agree that an insistence on doing things the way they've been done here or in Europe is counterproductive. The Guardian piece highlights the centuries of bloodshed that went into creating the current peace that the Western world enjoys - bloodshed surrounding religious and cultural differences, to say nothing of the slave trade and the extermination of native cultures in North and South America or Australia. And worse, in trying to contain Communism the West was frequently just as cynical as its Soviet rivals - the democratic process in the regions mentioned above (as well as Africa, South America, wherever) was usually subverted with the implicit or explicit approval of the US.
The point, though, is that even if the US didn't always live up to certain of its own ideals, it doesn't mean those ideals are necessarily useless. I sometimes think pundits get a little too bogged down in the actual terminology of Western politics, without thinking about the wider issues at play. The American revolution was (or is believed to be) significant for making explicit the idea that kings or presidents rule with the consent of the governed - this is an idea that you can trace across all cultures. Even Chinese emperors who didn't have the support of the people frequently ended up badly (just look at what happened to Wang Mang).
My argument is that Western-style democracy is based on this idea (much like I believe religion generally boils down to just being nicer to people), and it's associated with the West because it happened here first, and in a way that helped America become successful. Regular people want be able to live their lives, feed their families and, now that we nominally have all this free time, entertain themselves as they see fit. Governments should be able to provide these things, in the form of services and protection from external and internal threats - most poor people, in China, Africa or Mississippi, would rather eat than have ideology thrown at them, whether that ideology is free-market capitalism or socialism or something else.
This isn't a call for anarchy or Objectivism - it's the simple point that, in my view, if you allow citizens the chance to live their lives as they wish, without worrying about whether or not the playing field is level, then everything else falls into place: stability, prosperity and rule of law. If anything is tarnishing the image of the West right now, it's that we (especially here in the US) don't always live by that principle, and we're paying for it now with instability and income inequality. Because I'm biased, I'll note that the main problem is the hidebound ideology of the Republicans (in the interest of fairness, I believe the Democrats are too spineless to have an ideology).
If we allow one party of religious fundamentalists and Objectivist Randroids to derail our democratic process, as we're doing now, then of course Western-style democracy doesn't look too appealing. But I feel that if we in the West get back to living those principles of stability, safety and equality of opportunity, and don't concern ourselves with making sure Uganda or Cambodia align their political and economic systems with our own, then our model will become more appealing. Especially if we also don't force them to buy our crap.