I'm not sure how to contrast the two situations properly. I personally don't know enough about any of the systems to address the question with any confidence.
I don't know if I can supply an exact, full answer, but I will attempt to supply some context.
In Europe, the following communist states existed during the Cold War:
The USSR and Yugoslavia were both Federations which contained distinct, large national/ethnic groups. In theory, Ukraine, the Baltic States, Kazakhstan etc as part of the USSR were different countries with a unified foreign policy.
Yugoslavia and Albania were two nations which had large communist insurgencies and managed to regain partial or complete control over their respective territories at the end of WWII without the direct assistance of the Red Army. By contrast, Germany, Bulgaria, Czechoslovakia, Hungary, Poland and Romania were either occupied directly by the USSR or experienced some kind of coup sponsored by or loyal to the USSR. Yugoslavia is the most significant of these early communist states in the Cold War because of the "Tito-Stalin split" - the govenrment of the Yugoslav state, once loyal to Stalin, had irreconcilable differences in opinion with the government in Moscow, and refused to accept Moscow as the supreme authority in the Communist world.
The Western world for their part were generally quite happy to see signs of fracture in what had previously been thought of as the monolithic entity of Communism. With the rise of "Titoism", it became clear that national self-interest could override the broader, ideological interests of Communism. Yugoslavia became what some in the west would refer to as "our Communists". It walked a fine diplomatic line between the two, and traded with both the Western and Eastern blocs throughout the cold war.
Albania joined the Warsaw Pact initially, but later withdrew and sought a different foreign policy, aligned more with China at first, then later seeking a more independent path. As to why a country like Hungary or Czechoslovakia might be on the receiving end of a column of Soviet tanks over far more modest signs of defiance, but Albania could simply "opt out" of the Eastern Bloc as it were, the answer is two-fold. Albania always enjoyed some degree of autonomy from the USSR (the Soviets and Chinese at some point would be sending gift and competing for influence in Albania), and Albania is geographically blocked from the Warsaw Pact by Greece, Turkey and Yugoslavia.
The People's Republic of China ("Communist China") was engaged in guerilla war with the Republic of China ("Nationalist China") and later the Japanese throughout the first half of the 20th century. When it emerged victorious from the Chinese Civil War, it was initially closely aligned with the Soviet Union. Although making use of Soviet aid (and being helped substantially by the Soviet occupation of Manchuria), the Chinese were too large, too distant and too autonomous for the USSR to effectively control in the long term. They enjoyed a more equal status than, say, Bulgaria or Poland in the Communist world. The Sino-Soviet split occurred from about 1960 onwards, as a consequence of divergent priorities, differences of opinions about doctrine, Kruschev's policy of "destalinification" and so on. Relations broke down and the Communist world once again fractured.
European Communism, as mentioned above, was not a monolithic entity. It was however primarily based around Moscow, with the exceptions of Yugoslavia and later Albania. The collapse of each needs to be considered as distinct but related. I would therefore recommend individually investigating the fall of communism in each of these states, as well as going into some more detailed histories of the Cold War (I'm giving you the super cliff notes version right now). Since this post is already getting a bit long, I'll summarize the European side of things here:
Yugoslavia and the USSR, as mentioned previously, were essentially federations (although they may not have used this term exactly). Yugoslavia contained a series of republics which maintained separate governments. Throughout the 1980's, Yugoslavia experienced severe friction between these republics. Serbia, the "primary" state of Yugoslavia, attempted to strengthen Federal Authority at the expense of these sub-republics, and eventually Croatia and Slovenia attempted secession. This process kicked off the Yugoslav wars, where the various states of Yugoslavia broke away from the central government, and Serbia attempted to bring them back into the fold by force. Eventually, only Serbia and Montenegro remained, which separated in the early 2000's, finally killing "Yugoslavia" for good. The Yugoslav wars were not a revolt against communism per se, as happened in the other nations.
The USSR was the "last man standing" other than the disintegrating Yugoslavia. The transition from USSR to its successor states was alarmingly smooth, involving a failed coup attempt but no actual wars. The Baltic States had always maintained strong nationalist bents throughout their history as SSRs, and in the late 1980's they had been experiencing protests and agitations. In the wake of the 1989 revolutions and the loss of control of the Soviet Satellites, some Soviet Republics themselves started seeking greater autonomy - the Baltic States being at the forefront of this. Independence was declared over the 1990-1991 period, and the USSR acknowledged this independence in 1991. Following an attempted Coup, Ukraine would secede, after which the USSR itself dissolved into its discrete units.
Why is it that the Communist states in the East persisted, then, when those in Europe fell? This question I feel is flawed, because it ignores a more global context. Wikipdia provides two maps here of "Communist States during the Cold War" and "Communist States Today" to illustrate this concept. It was not merely "Europe" and "Asia", Communist states gradually collapsed all over the world. It is also not true that all Communist states in Asia survived - Mongolia (essentially a puppet of the USSR) transitioned away from Communism, and Cambodia (after a war and UN occupation) also lost its Communist government.
To a large extent, the reason Communism in Europe fell was because those in power allowed it to do so. Sufficiently oppressive and brutal regimes (think North Korea) may have been able to maintain control for far longer, or possibly indefinitely. The USSR itself became more open over time, first during Destalinification, then later during Glasnost and Perestroika. In China, the modern stability of the Party is to an extent based around economic prosperity, growth and the adoption of a more capitalistic system. At the same time, China has maintained a firm hand on its culture and dissident groups. I am not really familiar with Vietnam's modern history, so I can't comment so much on that situation.
The main sources I'm drawing from here are the following:
If anyone has some good sources for more detail about the Eastern and Global sides of this story (which I am familiar with on an abstract, but not detailed level), I'd be thrilled to check some of them out.
