While the New Testament authors looked forward to both a day...
While the New Testament authors looked forward to both a day of judgement and a new creation by God, they asserted that the possibility of freedom from sin and authentic human life were instituted by the atonement, and the sending of the Holy Spirit to the church, the Body of Christ.
Any Christian understanding of anthropology reckons with Jesus as the new Adam, the crucifixion of Christ on the cross which conquers the human fear of sin and death, the Spirit of Christ which makes his followers holy, and the nature of faith which makes it possible for humans to enjoy these gifts of God's mercy.
Any Christian soteriology is rooted in God's own sacrifice of his Son on the cross to pay the price of sin, the Christian hope for eternal life, the strength of the Holy Spirit to persevere in the face of evil and temptation, and the promised reign of God.
In Islam the essential problematic of the human relationship with God arises when the first humans, tempted by the Devil ( Iblis ), grasp after the created order as the ultimate reality, choosing the fruit of the tree rather than the command of God. As a result humans are exiled to the earth, away from the Garden which was to be their home and away from their stature as the highest of all creatures.
As a conscious choice this sin of choosing the created order is infidelity to God's command, making a person a kafir . When reflected in the elevating of the created order to the status of God this is the sin of shirk . The human condition which makes such infidelity possible is ignorance, jahiliyya , a condition which becomes pervasive in some times and places but which is never a necessary part of human nature.
Infidelity, idolatry, and ignorance were the primary characteristics which Muhammed found in his own time and culture. The first revelations which Muhammed received placed the reality of Allah, and Allah's judgement upon those who were idolatrous and unfaithful, powerfully before those who heard them. They called on people to know, and acknowledge, the one God, and to abandon immorality in order to be saved at the judgement day and to attain the lost Paradise.
This called for repentance, a change of heart.