I can't comment on Islam, but I can explain why Chinese christianity did not last to the modern day (of course, there are plenty of Christians now, but they only date back to European missionary activity).
First, about its origins. My source for the first part of this is a tablet in a museum in Xian (or rather, the internet translation of this: I couldn't actually read it, it's too decayed and in ancient Chinese, which I can't read anyway). The tablet was written by Persian (Nestorian*) missionaries. It described the last 200 years of Chinese Christian activity, setting up churches, evangelising, etc. However, from what it said, they don't seem to have made a huge number of converts.
According to a Chinese Christians I've discussed this with, the mainstream view of Chinese Christian scholars** is that the early churches were "very Buddhistic". What this means is, they became more and more similar to Buddhist practices, and eventually faded away as a strongly defined entity. In a German museum, there is a piece of art of Tang-dynasty Christians celebrating palm Sunday; other than the palms, they do not seem very different from Buddhist worshippers. A number of modern Chinese Christian leaders (read about the recent issues in Wenzhou and this will come up) have expressed reluctance to the Chinese governments aims of sinicising Christianity, because they believe that this could cause Christianity to lose any unique characteristics and thus fade away, as it did before.
Now, Nestorian Christianity returned to China in the Yuan dynasty, as it was the religion of certain Mongol tribes. However, it wasn't given government support, and being associated with foreign conquerers, again didn't make many converts. When the Mongols were expelled by the Ming, as with Tengrism, it was seen as a foreign Mongol religion, that should be expelled from China.
As I said, I don't know why Islam managed to create a strong community (I assume you are referring to Huizi; with the Uighers it's the same way it spread to central Asia generally, though the silk road), only why Christianity didn't. I'd be curious if anyone knows the history of the Huizi?
*Bear in mind that the "Nestorian Church" probably wasn't actually Nestorian in doctrine, they just tolerated Nestorians while the European churches didn't.
**As I said, this is (I believe) the mainstream view of Chinese Christian scholars. I feel it's important to point out that it is used as a narrative of resisting the government; it's possible therefore that this view is unreliable. I don't know of any non-Christian, Chinese historians who study the history of Christianity in China, to compare it to. It seems like a reasonable hypothesis, but I feel I should point this out.
So, I've done a bit more looking around on this topic, and discovered something I did not know (and I find it very interesting that no Chinese Christians have ever told me this). When Emperor Wuzong made Buddhism illegal in the great Anti-Buddhist Persecution of 845AD, he also banished all Zorastrians and Christians. "As for the Tai-Ch’in and Muh-hu forms of worship, since Buddhism has already been cast out, these heresies alone must not be allowed to survive. People belonging to these also are to be compelled to return to the world, belong again to their own districts, and become tax payers. As for foreigners, let them be returned to their own countries, there to suffer restraint." Tai-Ch'in (or Da Qin as modern Pinyin would say it) means Roman, and Christians were generally referred to as Romans (well, actually by this time it generally referred to Syria specifically). You can read the pronouncement here: http://www.religion-online.org/showchapter.asp?title=1553&C=1363