Christianity and Islam are very similar on paper. The differences are in the rendering, which reflects the history and the culture of the areas in which each is administered. The Christian West has been under the influence of the secular democracies that emerged from the rise of Enlightenment values and secular humanism, and has been dramatically influenced by its rational ethics.
Hence, Christians no longer execute people for homosexuality, adultery, witchcraft, fornication, apostasy, impiety, blasphemy, and other crimes against Yahweh, whereas Muslims are still free to kill such people.
But the very fact that they share all of those values even if they don't act on them the same way is evidence of their ideological similarity. The fact that they are not free to indulge those values in the West is not a result of Christian values or its church, but of the secular humanist influence in the West.
If you extract Christianity and Islam from their surrounding cultures, they appear very similar.
Christians and Muslims each revere a Semitic desert god, Yahweh and Allah, that is an angry, petty, vengeful, jealous, judgmental, capricious, pestilential, prudish, strongman that requires worship and submission.
Believers of both attend temples (Mosques or churches) and obey paternalistic, misogynisitic clergy.
Both religions embrace magical thinking, mythology, dogma, the supernatural, and ritual.
Each feature demons angels, prayer, an afterlife, a judgment, and a system of reward and punishment after death.
Each has its now centuries old holy book of internal contradictions, failed prophecies, and errors of history and science. I'm not as sure about the Qur'an, but it likely also contain vengeance, hatred, tribalism, violence, and failed morals that endorse slavery, rape, infanticide, and incest.
They each think they have the right to determine who should be allowed to to have sex with whom how, who should be able to marry whom, and what women must do regarding their bodies.
Both are patriarchal, authoritarian, misogynistic, sexually repressive, anhedonisitic, atheophobic, homophobic, antiscientiific, use psychological terrorism on their children, have violent histories featuring torture, genocide and terrorism, and demand obedience and submission.
Each consider faith a virtue and reason a problem.
Each has a history of opposing human rights and science.
Each advocates theocracy over democracy.
With all of these similarities - and that is a lot of parallels, most not found elsewhere - why should these two appear so differently where they are applied if not for the reason I just gave? The difference between America and the Middle East is not due to the differences in the holy books of Christianity and Islam
If you traded the ideologies out, and put Christianity in Saudi Arabia and Islam in America, the results would be the same: Christian Arabs cutting off hands and heads, pushing homosexuals off of Towers, doing honor killings, genital mutilation, suicide bombings, and flying buildings into airplanes, and Americans going door to door asking if you know Mohammed. America would still be a secular state with a Muslim majority forced to tolerate "infidels" thanks to humanist values, and Saudi would still be a brutal, intolerant theocracy, but a Christian one instead.