Abbadon and others made a very good point about the barbaric and violent actions of nations that called themselves christian. It just shows that people or groups will act according to their dispositions first and foremost. Then they'll seek to justify their actions by whatever means gives them the most support. Now for the militant islamists, its many of the passages in the qu'ran. I don't care about being politically correct. It is very plainly commanding the killing of all infidels wherever they may find them. Then there are many hadiths that reinforce these thoughts as well as a few ones that are anti-semitic.
Many moderate Muslims though, a handful of which I spent more than a year with while I was at university, will take the same qu'ranic passages and try to interpret them with the historical context of their origins in mind. They don't see the need to apply those passages in the conditions of today's world. IMHO because they are not inclined to violence and intolerance. If I got it right, they reason that the "lesser jihad" ( to which all those passages refer to) was sanctioned at the time to prevent the complete obliteration of the umma. With a less threatening world, they can make the "greater jihad" of the heart and on social injustices the important focus.
Work on eliminating the perceived (dare I say real) injustices and exploitation of many muslim populations, and the fanatics will have less causes to which they can rally like-minded ones. Then the umma, who are as a whole mostly peaceful, can work on reforming and reinterpreting their religious world view in accord with the current world order.
As to economic prosperity, the islamic states really started falling behind from the industrial revolution onward. Qutb was a very influential writer that kindled the aversion to western culture and unfortunately "modernity" has been equated for all practical purposes to many facets of the west. So that definitely has contributed to the disparity but much of it also has to be blamed on the rulers of those states as well.