There are several important differences though. Christian teaching doesn't command theocracy and, historically, Catholic states generally tolerated minority religions, especially in comparison to other contemporary nations. Religious tolerance and freedom of conscience is a Christian idea.
Also there is no such thing as a "Church" in Islam.
Muhammad: Kill the infidels, (but let me keep the pretty Jew girl as a slave)
Be that as it may, it took hundreds of years before that was codified and civil rights were granted to non-Christians. The Islamic world, in many ways, has not passed from that medieval world but those reasons are more complicated than simply condemning their religion. That's why this election is so important, that's why the constitutional requirements of protecting minority rights is so important. This is what is before the Iraqis and by all reports they seem, so far, to be embracing that idea.