I came across this interesting article describing Church of the East recently, which apparently had a long history in China. Would Church of the East give more influence to China compared to other sects of Christianity?
Completely lose influence.
They have been politically cleaned up many times in history.
This religion has been confined to a very small group of believers: ethnic minorities.
Moreover, missionaries also face many problems: poor translation, the theory of original sin contradicts the theory of good nature in China, and too much borrowing of Buddhist concepts leads to being regarded as Buddhist heresy.
So the spread of Christianity in China later had nothing to do with Nestorians.
Out of all the Christian sects, China should encourage the Chinese Orthodox Church (which was granted autonomy by its mother church, the Russian Orthodox Church, in 1957) over the others. Unlike Catholicism, where the Pope is sovereign, the Orthodox practices Caesaropapism where the head of the church, the Patriarch, is subordinate to the head of state. Protestantism does not believe in any hierarchy as the relationship with God is personal and so disavows the Pope or any other authority over individual views on morality. The Central government is better able to exercise power with Orthodox Church to keep down the more Western influence via Catholic and Protestant sects and grow even closer to Russia and Eastern Europe.
The problem with this assumption is that China has been guarding against Russian influence. In China, the spread of Orthodoxy was completely dependent on the expansion of Russia.
And the atheist dominated regime is also unwilling to see the church encroach on social leadership.The influence of the Church has never been limited to within the church.