The question of what is more important for mankind is the birth or death of Jesus Christ, is not correct. First of all, it is necessary to speak not only about the importance of the New Testament events for humanity, but, first of all, about the purpose of the historical New Testament events from the life of Christ.
The very moment of the Incarnation was necessary for the salvation of all people, the reconciliation of man and God, deliverance from the power of hell (into which all people fell until the time of the death of the Savior on the cross). Christ is incarnate to give the opportunity to regain the opportunity to be with God after death.
It is not worth talking separately about the birth of Christ and about his death. All this is aimed at one action - the salvation of man. Although, in Orthodox dogmatic textbooks, one can find information that the salvation of a person took place through the death on the cross of the second Person of the Holy Trinity. This is really so - through the death of God, a person acquires the possibility of eternal life with the Lord after his death. However, if it were not for the very fact of birth (the incarnation of Christ), we would not talk about the sacrifice on the cross.
Now we can say about the importance of the very incarnation (birth) of Jesus Christ from the other side. God Himself takes on a human body, human nature is hypostasized in the single hypostasis of the second Person of the Trinity. The human being is sanctified, made blessed. This also needs to be considered when we talk about the birth of Christ. One of the hierarchs of the ancient Christian Church said that God became man in order for man to become God. Of course, man cannot have a divine nature (being), but he can become "God" by grace.
