The Nature of God
Christians believe in a God that is relational - that is, God desires a relationship with us and in fact, God is actively pursuing that relationship. In addition, God is internally relational, as evidenced by the Trinity. Muslims view Allah primarily as a master and themselves as servants of that master. Allah has no need of a relationship with us.
Christians view God as 'love' with God having love for everyone - not just Christians - and capable of being loved in return. Allah can be described as loving (occasionally) but this love is conditional (for those who obey Allah) and in no way guaranteed.
The Christian God guarantees salvation for those who accept Jesus Christ. In Islam, there are no guarantees - except possibly for those who die for the faith. Allah is free to do whatever He wishes regarding salvation.
The Christian God is a holy God, meaning that He cannot tolerate sin. This is why the sacrifice of Jesus on the cross was necessary - to bridge the gap between a holy God and us as sinners. Allah, on the other hand, holds to no absolute standard and is free to do whatever He pleases.
Islam and Christianity Compared
Comparisons between Islam and Christianity can be tricky. A Muslim might view Christianity as a sort of corrupt early manifestation of Islam. A Christian might view Islam simply as a false religion. With such contrasting perspectives, there can be significant disagreement over some very simple facts. Nevertheless, there are a number of areas where Islam and Christianity can be contrasted and compared in a manner that most Muslims and Christians can agree upon. Note that in claiming the roots and prophets and god of Judaism and Christianity as their own, Islam actually accepts none of either. Only the word as given to the last prophet, Muhammad, actually counts. The rest is just for show.
Here are some comparisions:
God: Although Christians believe that there is only one God, God manifests himself in three persons: Father, Son and Holy Spirit. Muslims consider this blasphemous. There is one God and only one manifestation. Given the differences in the 'nature of god' as propounded by Muslims vs Christians, suffice it to say that that the Muslim and Christian gods cannot be one and the same.
Jesus: Jesus may be a prophet in Islam, but he was only a man. To Christians, Jesus was wholly God and wholly man and was crucified to atone for the sins of the world. Muslims do not believe that Jesus was crucified at all. Some believe that Judas was made to look like Jesus by God and was crucified instead. So the Jesus that Muslims 'believe' in is simply not the Jesus that Christians believe in.
Atonement: Christians believe that the sacrifice of Christ on the cross turns away the wrath of God from our sin when the sinner accepts, by faith, Christ's sacrificial work on the cross. There is no atonement in Islam other than a sinner's confession and repentance.
Bible: To Christians the inspired and inerrant Word of God. To Muslims the respected word of prophets, but corrupted over the years and only correct when in agreement with the Quran.
Quran: To Christians simply a work of Muhammad or his followers. Neither inspired nor verifiable in its transcription from the original. To Muslims, the final revelation of God, given to Muhammed via the angel Gabriel without error.
Original Sin: Christians believe man is sinful by nature, inherited from Adam. Muslims believe man is sinless by nature until they rebel from God.
Salvation: Christians believe that salvation is a free gift from God, never to be earned by works but by faith alone. Muslims believe that salvation is earned by following the doctrines of Islam.