I think what broke the power of the church was an increase in the overall quality of life in Europe, a shift that stemmed from an emergence of the middle class, an emergence of a free market, advancement of science and rates of literacy. The Church, whether it happens to be a mosque or a synagogue, tends to lose much of its leverage when people start to realize that faith isn't the only thing to live for. There are exceptions of course, where even the comfortable, healthy and educated remain fanatics, but as a whole, I believe it's the above mentioned elements that broke the monopoly religion had on governing the way average people thought and behaved.
Personally, I think Islam may have set its people apart permanently. They live in a world full of new possibilities but tend to remain of the belief that Allah is not just the biggest thing around, but the only thing around.