In history, Buddhists have been both tolerable and intolerable of Christians of the Church of the East. From
wikipedia:
As far as an “Eastern Christian doctrine on Buddha”, there is no such specific doctrine other than what is the general teaching on all such men, good or bad, as explained by St. Paul in
Rom. 2: 11-16:
So, Christ’s judgment of Buddha (or any other Gentile for that matter who lived prior to Christ, and those who lived after Christ but were unaware of Christ) is based in accordance with the “natural law”, that is, the law written on their hearts and dictated by their conscience.
As far as the religion named after him, Buddhism, it has both truth and falsehood mixed in with each other. Buddha said: Look not to me, but to my teaching, whereas Christ said: Come to me, for I am the way, the truth, and the life. Buddha said: Be lamps unto yourselves, whereas Christ said: I am the light of the world. The Buddhist religion is religion-centric, whereas the Christian religion is Christ-centric. In Christianity, instead of the founder pointing to the religion, the religion points to the founder.
Here is an ancient cross of the Church of the East, known as the St. Thomas cross, which depicts the triumph of the luminous religion of Christianity over the lotus-flower of Buddhism, and the dense cloud of Islam:
aina.org/books/bftc/3fb35270.jpg
God bless,
Rony