There are a few significant differences:
1. Soteriology (doctrine of salvation)
While both faiths teach that man is guilty and that there is a day of judgment, they differ in how you can succeed on the day of God's judgment. Islam teaches that your works and sincerity must be sufficient, and then Allah will most likely forgive you and allow you into heaven, though you can't be sure. While some say that Islam is not a religion of works, in practice, it is taught that way. In fact, this insecurity and unsureness about one's eternal state drives many to suicide killing, because certain sects of Islam also teach that if you die as a martyr, you guarantee your entrance into paradise (heaven).
Christianity clearly teaches that salvation can not be earned through good works, but that it is a free gift, as described in Ephesians 2:8-10:
For it is by grace you have been saved, through faith—and this not from yourselves, it is the gift of God— not by works, so that no one can boast. For we are God's workmanship, created in Christ Jesus to do good works, which God prepared in advance for us to do.
2. Jesus and Mohammed had some similarities, but they lived very different lives and taught very different messages.
For a superb comparison of the two, I recommend Mark Gabriel's Jesus and Muhammad: Profound Differences and Surprising Similarities. The author is a former Islamic Ph.D. who was an Imam and taught at the most prestigious Islamic University in the world before leaving his faith (because as an academic, he was persecuted and tortured for asking questions), and later became a Christian. Though he does have a bias, he is very knowledgeable in Islam, and is not judgmental or superficial like a lot of Christian writers on Islam.
Reading this book really opened my eyes to the vast differences between these two men. I found Jesus' teachings and life to be incredibly superior to that of Mohammed, who, among other things, went on many jihads, killing his enemies, and married many women, including a 6 year old girl (whom he generously waited to have sex with until she was aged 9).
3. How the faith is spread
Islam teaches that their faith is spread by both teaching and by the sword - if a people don't convert or pay taxes to the Islamic ruling government, they can and should be executed. While some moderate Muslims contend that this is not true, it is most certainly taught by the more conservative (not just the extremist) Islamic organizations, and it is practiced around the world in most modern Islamic nations.
Christianity's teaching is that the sword can never spread the gospel, but rather, only preaching, reasoned argument, and loving service.
2 Corinthians 10:3-5
For though we walk in the flesh, we are not waging war according to the flesh. For the weapons of our warfare are not of the flesh but have divine power to destroy strongholds. We destroy arguments and every lofty opinion raised against the knowledge of God, and take every thought captive to obey Christ
James 3:13
Who is wise and understanding among you? Let him show it by his good life, by deeds done in the humility that comes from wisdom.
4. Separation of Church and State
Islam's view is that there is no such thing as separation of church and state. The religious leaders should be running the government, and the laws of Islam, both moral and religious, should be those that are made into law. However, there is a growing moderate Islam which is questioning this doctrine.
In Christianity, of course, there is a broad range of positions on church and state, but one of the most enduring across time is now being espoused by those who support the Bible's "Cultural Mandate."
Biblical Principle v. Religious Principle
A key distinction of the cultural mandate is that proponents are not interested in legislating religious laws, such as Sabbath attendance or blue laws, but rather, are interested in taking timeless practical principles, many of which are not the sole property of Christendom, and applying them within a biblical framework.
For instance, the principles of an honest and independent judiciary, criminal sentencing accompanied by restitution and the possibility of mercy on the penitent guilty, and the fair treatment of prisoners are all considered to be "biblical principles." This may be a misnomer, since these principles have also been elucidated by other religions and ethical systems. But what makes them biblical to the cultural mandate proponents is that they are in the bible AND fit within a larger biblical framework.
Appeal to Reason v. Appeal To Scriptural Authority
Another key distinction of those supporting a cultural mandate is that, in the public arena, proponents feel that they must convince and argue for their worldview, not from the bible as an authority, but from natural law and common ethics. As an example, they would argue to criminalize murder not because it is condemned by the bible, but because it violates the self-evident right to life that all men deserve, and because it violates the ethic that we should not harm one another or society. Even if cultural mandate proponents are biblically motivated, they respect the idea that appeals to religious authority should not carry weight in public policy discussions.
5. How they view Jesus
Of course, Christianity views Jesus as unique, God incarnate, who once and for all paid the price for sin so that we can be forgiven and given a new and abundant life here.
Islam views Jesus as a prophet, but denies many of his teachings and the biblical teachings about him. Also, since they view the later prophets and their teachings as more authoritative, they value the teaching of Mohammed over those of Jesus. They consider the deity of Jesus a polytheistic idea which denies the existence of one God - while Christians assert that the Trinity is not pantheistic or teaching multiple Gods, Muslims believe that it is, and therefore, is false.
