The differences between Islam and Christianity are not just about the laws of nature. They’re also about laws for man.
Christianity has its own religious law, laid down by Moses in the Old Testament, though much of it does not survive Christ’s revisions. But Christianity also has a long tradition of coexisting with secular systems of law. This comes from the Roman context, where there was an established, codified Roman system of law which Christianity did not seek to overthrow. This, as I understand it, is part of the significance of Christ’s admonition to “render unto Caesar that which is Caesar’s.” So the idea of religion as the source of law was not well-established under Christianity. Or to be more exact, religion is viewed as source of general moral principles, but there is plenty of room for debate on what those principles mean and how to translate them into specific laws.
By contrast, Islam recognizes no room for any law other than what was supposedly revealed to Mohammed, and that is the source of a whole lot of trouble. The explicit argument offered by Islamists against representative government is the complaint that laws voted on by the people are laws created by man, whereas God is the only one who can make law. Similarly, one of the main issues of contention in newly created governments across the Middle East—Afghanistan and Iraq, as well as Egypt, Tunisia, and Libya—was the question of whether Islam should be cited as the sole source of law. Then there is Saudi Arabia, where the Koran is the constitution.
But what is really telling is the concreteness of Islamic law.