It seems like peasant revolts were unlikely to succeed in most places, but China seems like an exception. The Han were perhaps not destroyed by the Yellow Turban Rebellion, but it was probably one of the biggest factors in their downfall. The Yuan were likewise largely overthrown by popular resistance from the White Lotus / Red Turban rebels, and the Hongwu Emperor himself was from a peasant background.
This seems like it's pretty different from most other places in Eurasia: a Japanese shogun might have worried a little about rebellious peasants, but they didn't regularly pose anything like the potential threat posed by rebellious daimyos. Likewise an English king was more likely to fear rebellion among the baronial class, a Roman emperor feared powerful generals/governors, a Persian shah feared his brothers and perhaps satraps, etc.
I'm not saying that peasant revolts are a complete anomaly outside of China, nor am I saying that the sorts of elite rebellion that seem more common outside of China are completely absent within it (such as the An Lushan revolt), but overall, it seems like in China instability came less from elite rebelliousness and more from popular rebelliousness than elsewhere. Is this perception accurate? If so, why?
There are a variety of reasons for this. I'd say that they would be in this order of importance.
China relied on large standing armies made up of peasants for large parts of its history, rather than having armies that would be formed ad hoc as crises occurred. This meant there was a large peasantry that was experienced militarily, and that revolts would form around them.
Chinese culture of course emphasizes the status of the state as a whole universe, with the higher up officials being responsible for the people, and the emperor being responsible as the connection between the heavens themselves and all of the people. The upshot of this was that there was very much a sense that it was the duty of leaders to look out for the peasantry, and that the order of heaven was out of whack if they didn't do so. This gave a very clear rallying point for peasant revolts, and a clear reason for them.
You hit the nail on the head when you state that noble rebellion was a larger issue elsewhere. China's nobility was continually de-emphasized for much of its history until by the early 1000's-1100's it became a non-issue. This meant that the focus of discontent would be on peasants v. the government, rather than peasants v. local nobles. So while the revolts may have been similarly frequent, they generally had larger goals.
This is a real interesting question, and while my answer is based on my perception of it, it would need a lot more quantitative research to figure out just how to compare the success of revolts in the respective countries.
Besides reading any number of books on Medieval/Early Modern European Peasantry and revolts, I'd recommend Hucker's China's Imperial Past for a whirlwind overview of Chinese history.
I don't see how peasant revolts were that successful in China. Only two major dynastic founders, Liu Bang and Zhu Yuanzhang, came from peasant origins. The White Lotus Rebellion arguably won, but the Yellow Turban Rebellion was crushed.
However, I understand your point. Compared with Japan, Europe, and Persia, there's less of an elite threat to the center. For the imperial period, anything resembling feudalism or decentralization is basically gone. In most Chinese dynasties, there is nothing like an institution of daimyō in Sengoku Japan where landowners or nobles have their own armed forces and manage the land independent from the government. There of course are often rebellious governors, as well as areas where local aboriginals might rule, but these are themselves institutions. This limit on nobility/feudalism (the latter being very different from the European institution but a good word for lack of others) began around the 200s BCE, when the Qin Dynasty abolished the fengjian (or feudal) land administration system of the Zhou Dynasty in favor of direct rule in the junxian (or commandery) system. The resulting Han Dynasty did employ a mix of both, but soon favored the junxian system more. Certainly by the 1000s, the fengjian system was gone.
For Japan, I would point out that in Japan, elite infighting was not particularly common. Until the Sengoku period, violence was usually short and sustained, rarely lasting more than five years. So while Japanese shoguns faced threats from regional lords (the word daimyō arriving fairly late), I think you should not overestimate this issue.
So your perception is accurate only in the sense that peasant revolts seem more common than elite rebellion in China, because elite power and rebellion was comparatively limited when compared to the rest of Eurasia. My explanation would focus on ideology: if centralization eliminates the elite in the periphery, the only sort of unrest is probably going to be of the peasant variety.