An interesting comparison.
I remember it being all trendy in some circles in my former life as a Liberal Protestant minister that being a Christian Buddhist was all the rage, or at least taking prayer meditation techniques and such from Buddhism. Thomas Merton, in particular, got really sucked into this prior to his death. I believe had Merton lived past the height of 1960's weirdness that he may have backtracked on this, but, tragically, we will never know.
I never quite understood the fad, nor did I think it was really compatible with Christian thought and life. We are made in the likeness and image of God and so, if the ultimate goal of life is the extinguishment of the self, then that means an extinguishment of something made in God's image. That's a problem. Likewise, while we do not deny that suffering exists, and that there can be redemptive suffering, this does not stem from a world that is completely bad or evil. We believe God made the world and called it good. While sin has entered and corrupted the world, it is still a creation of God, so to say that all created matter is inherently evil and that the ultimate goal is to extinguish the self and remove oneself from the evils of the world, that's not quite Christian either, particularly since Buddhism is not concerned with God one way or the other.
Everything flows out of God and God will return everything unto Himself in the Ages of Ages, as it says in the Eastern liturgies. That is a very crucial and fundamental difference. There is Absolute Truth (which is ultimately God) and it is quite apart from whatever the individual believes to be truth.
In any event, it is worth a read.