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 talk not only about the importance of New Testament events for mankind, but, first of all, about the purpose of 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, the deliverance from the power of hell (which all people fell into before the death of the Savior on the Cross). Christ incarnates to give the opportunity to regain the opportunity to be with God after death.
Do not talk separately about the birth of Christ and his death. All this is aimed at one action - the salvation of man. Although, in Orthodox dogmatic textbooks you can find information that the salvation of a person occurred through the death of the cross on the second Person of the Holy Trinity. This is true - through the death of God, a person acquires the possibility of eternal life with the Lord after his death. However, if there had not been the very fact of birth (incarnation of Christ), we would not have talked about the sacrifice of the cross.
Now we can say about the importance of the very embodiment (birth) of Jesus Christ on the other hand. God Himself takes upon himself the human body, in the single hypostasis of the second Person of the Trinity, human nature is demonstrated. The human being is sanctified, made graceful. This also needs to be considered when we talk about the birth of Christ. One of the saints of the ancient Christian Church said that God became man in order for man to become God. Of course, a person will not be able to possess a divine nature (being), but he can become “God” by grace.
