I'm not sure the premise is correct. We can get a rough idea of how much space a country occupies in English-language media for a Google search. This is a crude measure, but I think it will give a decent idea. A search for Tibet only brings up 94 million results, whereas a search for Palestine brings of 224 million. Venezuela has 1.3 billion (in fairness, its status as a country is not as disputed by other countries as the other two, and its search results are likely combining English and Spanish at the very least). While this is indeed a very rough proxy, "Tibet crisis" has only 4,400 results compared to 24,600 for "Palestine crisis" or 3 million for "Venezuela crisis". Even something like "Sudan crisis" has 1.2 million results.
If we compare Google news results, Tibet has 4.8 million, but Palestine has 17.8 million, Syria has 58 million, Venezuela has 569 million, and so forth. I'm not totally sure whether you consider the issues in these countries worse than in Tibet, but it does show that many other countries are getting more attention.
If we do a direct comparison to "Falun Gong" or "Uigur" or its variations, there are far fewer, but that's to be expected: those are groups within countries, and not countries themselves. We can try to get at the relative frequency by comparing "Tibetans" instead. This has 61,000 news results, to 44,500 for Uighurs and 35,200 for Uyghurs, likely with some overlap in articles that define the two spellings. Other spellings may turn up even more results. Falun Gong, however, does have many fewer results.
Google trends bears out the same pattern. For instance, "Tibetans" vs "Uyghurs" (essentially on par, before accounting for alternate spellings), or "Palestine" vs. "Tibet" (about three times more common to search for Palestine) or "Sudan crisis" vs. "Tibet crisis".
This still doesn't account for whether European or US governments are devoting more attention to one issue or the other, but it does suggest that (a) the cause of Tibetans represents a small portion of English-speaking human rights concern abroad, as measured by news and Google result frequency and (b) that even when comparing the cause of Tibet to the cause of Uyghurs, it doesn't necessarily have more traction.
If there is still a disparity in favor of Tibet that's not captured by this comparison, though, it could be due to the following:
- Anti-Muslim sentiment is more common in the West than hatred of Tibetans. This could motivate some people to be less sympathetic to Uighurs.
- People are often more sympathetic to a foreign country unjustly invaded than to a group unjustly persecuted by their own government.
- Tibet, Nepal, and that general area have long had a mystical association among Westerners who tend to exoticize the region. This could contribute to them being viewed more positively.
- The harm in Tibet is, by some measures, worse. Although it's ultimately subjective which is worse due to the need to compare such incomparables as imprisonment, occupation, and death, some people estimate that as many as 1 million Tibetans have been killed in the course of Chinese rule. Although some Uyghurs have also been killed, particularly in Chinese internment camps, I haven't seen numbers close to that (though it's hard to be sure, because the government is not forthcoming).
- In the case of Falun Gong, the degree of persecution is unclear, due to the secrecy of the Chinese government. Some people estimate thousands of deaths; others, tens of thousands.
And perhaps, more positively:
- Helping oppressed people isn't a zero sum game. Activists and even governments may not feel that they have to figure out who the most disadvantaged group is and ignore wrongs done to the rest of humanity.
Some side notes:
Is the amount donated to Nepal really so large? I see an estimate of 4.1 billion USD, which seems high. But Haiti received 13 billion USD after its earthquake, and Indonesia received 6.5 billion USD after its tsunami. Haiti even has a smaller population. It's not clear that Nepal did receive an extraordinary amount, let alone because of spillover from positive sentiment toward Tibet.
It's difficult to tell whether Bhutan does have a positive image because of association with Tibet. The two things you mention aren't necessarily evidence of that. Bhutan is carbon-negative, due to an extremely agricultural society and extremely strict laws about development; as for the gross national happiness index, Bhutan's position has little to do with Western sentiment and a lot to with the fact that the concept was coined by the King of Bhutan and is measured by a research institute in Bhutan! (See also, the US is the most free country on Earth, according to US politicians).