Greetings in that Divine and Most Precious Name of Our Lord and Savior Jesus Christ!
As much as they'd hate to admit it, Buddhism is a legalistic religion like most of the Old World faiths.
Essentially, the Buddha taught that human beings are caught in a struggle of desire (self-will) and this is similar to the fracture observed by the Orthodox Fathers. This desire entangles us until we die continually, and each successive life cycle we work out more and more of the tangles of desire, the bad kharma (wages of sin) and inevitably achieve a God-like state of stillness, silence, eternal bliss, instead of the chaos of sin and desire.
This is realitistically similar to Moses' Law if we condense all the life-cycles of the Buddhists into a single human life-span. These are discussing the same concepts, the internal consequences of negative free-will decisions. The problem, much like with the Law, no one of us can willfully cease the chaos of Sin.
Jesus Christ came precisely to send Grace through the Divine Mysteries and by His power heal us from Sin, and keep us from Sin, and give us Eternal Life in His Kingdom by His merits, not our own.
The Buddhists have a lot of valuable philosophical insights about life, spirituality, and the human condition, we shouldn't reject their observations outright, however when it comes to Salvation, we know only can Jesus Christ give us this by His gift.
The Buddhists would say that is fine, that Christianity is how we may have discovered to remove our kharma.
I like a recent statement by the Dali Lhama:
Religion, he says, is like tea, and compassion and ethics are like water. Water is the foundation for tea, and so religion is compassionate and ethical. However, tea is spiced with Grace which heals, warms, sustains. This is the key part, he explains that while mankind can live on water alone, that is, without religion. Of course, just like water, while man may be able to survive (barely) without the tea of religion, we absolutely need to water of compassion and ethics to survive. It is these kinds of insights that the Buddhists have which are invaluable