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Religions do not exist in a vacuum: they are colored by the nature of the larger world in which they exert influence. Christianity was the way it was in the 1400's not simply due to the weight of its own influence, but because of the lack of more advanced influences in its sphere. The Enlightenment and Renaissance came about in reaction to ages of medieval repression. The Church as it had existed for many hundreds of years previous to that time came along only reluctantly into modernity. But come along it did.

Islam on the other hand has stagnated - it has remained stuck in the 9th Century - since the 9th Century - and has proven absolutely resistant to the encroachment of a single modern idea.

Christianity (and Judaism, and Buddhism for that matter) are more advanced not because they got a "head start" but because they are open to the ideas of human progress and the primacy of individual liberty - concepts that Islam explicitly rejects.