I'll tell you the primary power difference between Christianity and Islam:
1) Jesus said, "Render to Caesar what is Caesar and to God what is God's". This cleaves the core religion from government. Jesus was a single, poor itinerant preacher who was crucified between thieves. One can be a good Christian and accept a separation of church and state.
2) Muhammad was a political and military leader who created a religion which also was a system of government. There can be no separation of church and state in Islam. One cannot be a good Muslim and accept a separation of mosque and state.
Henry VIII was sick of being pushed around by the Catholic Church, a competing power center to his own. So he formed the Anglican church and set himself as the head of it.
The Founders said, in the First Amendment, that "Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof". They too understood organized religion as a competing power center and knew not to allow one to spread its roots to take hold of the government. Such a dichotomy is nonsensical in Islam.