To be honest I don't buy into this "Islam needs to grow up" line. There are several fundamental differences between Islam and Christianity.

1. The Koran is the infallible word of the God, the Bible is an anthology explicitely compiled by priests and Bishops, leaving aside the OT the NT is NOT an actual source of absolute authority, because there is no "Book of Jesus" i.e. no direct word from God. It's an important point and it means that Christians can make judgements without actually going against their Holy text as a whole, that's not possible with the Koran because it is absolute. This is not to say that Christians have not claimed Biblical infallibility but it manifestly is not built into the text itself.

2. The rise of the two religions was completely different, Christianity is a religion of the poor and dispossessed as well as the wealthy, it is all inclusive and it's principle figure pointedly refused to assume any Earthly Power, in direct opposition to Islam where the principle prophet was a powerful military and political actor in his own times.

3. Christianity and Islam have subtly different views on issues such as free will which further affect interpretation. Jesus was decidely oblique when it came to issues of salvation and the nature of God, the issue of exactly what is required in order to enter heaven remains one of stiff contention among Theologins because we have no authorative account of what Jesus taught.

Ultimately the enjuring images of Christianity are the fisherman, the shepard, the carpenter and the sacrifice on the cross, none of which are images of power. None of this makes Christianity better than Islam but it makes the two fundamentally different and I personnally believe it makes a direct comparison of their development innaplicable. Particually as Islam has already had several peaceful and enlightened periords.

If you want a comparison Judaism is a much better bet but that religion has not had the same political clout as Islam for a long time.