Comment2: Since Islam honors the old and new testaments as sacred works of divine revelation, and since they believe God is God, then Allah did do that and Christ died for us all in their view also. Redundancy is not desirable.
Comment3: So Islam seems to be a parallel or alternate track to the Bible, not an "improvement" on Christianity.
My Response: Allah means The Deity, and therefore God.
We believe that all religions originate from the same source and thus are common in their essence. Each successive prophet came to proclaim, preach and purify the message, restoring it to its pristine glory. Prophet Muhammad also came with the same message of unity of God, of love and compassion, of patience and perseverance, explaining the temporal and eternal, the reality of this life and the undeniability of the hereafter, the responsibility of each for his/her own beliefs and deeds.
We believe that Jesus was never crucified, neither do we believe in doctrine of original sin. The understanding we get from the Quran is quite different.
Links below are some of my earlier responses on these topics:
Allah is God, The Deity http://islam-qna.blogspot.com/2008/12/allah-is-god.html
Original Sin http://islam-qna.blogspot.com/2008/12/original-sin.html
Man central to creation or not http://islam-qna.blogspot.com/2008/11/man-central-to-creation-or-not.html