hi dig,
I am sure there is some economics mixed in, although it seems to me it has more to do with a country like Saudi Arabia funding madrassahs and fuelling hardline clerics than some intrinsic advantage of the European landmass.
Lest we forget, the Eastern and Southern Mediterranean was wealthier than the Northern Mediterranean from the birth of civilisation, through the Greek and Roman eras, all the way to the fall of Constantinople. Wheat was discovered in Turkey and formed the basis of cereal-based urban development along the banks of the Tigris and the Euphrates. Consider the fertility of the Nile valley and compare the scale of Stonehenge and the pyramids. Greek civilisation in its extraordinary glory curled from Greece along the coastline of Asia Minor, through the Levant to Egypt. The Ptolemys were Greek pharaohs, after all. North Africa was the granary of the Roman empire. The Pirenne thesis sought to describe why the wealth of the Roman empire disappeared Eastwards as Rome declined. Compare the lives of the emperors in Byzantium with that of Charlemagne. They took mass in Hagia Sophia. He took it in Aachen Cathedral, which would fit in the hallway.
From my view you have inverted cause and effect. Western Europe's modern economy grew out of social and governmental developments that permitted curiosity, stability and continuity. Monarchs worked out how to free themselves from religious shackles through arguments over the investiture of bishops and the abuse of indulgences, thereby leading to a secular polity. The ideas of Greece return to the West from Islam during the scholastic period and free Western philosophy from the lock of Biblical interpretation. The printing press appears and spreads these ideas. Scientists detached themselves from the predefined truths of religion during the period from the Copernican to the Darwinian revolutions. Banking arrangements developed beyond the purview of clerics in places like Florence, Venice and Holland, as well as amongst Jewish minorities. Anglo-Saxon ideas of individual freedom find their expression in documents from Magna Carta to the US Constitution leading to the constitutional interpretation of religious freedom as a matter of personal conscience.
As these things occur, they lay the groundwork for the period of discovery and the economics that emerges from it. Intellectual flexibility on a stable, secular social backbone delivers wealth.
Whereas Islam went in the opposite direction. The Arabs inherited the Greek East and its systems of enquiry. They found themselves in the position to synthesize Greek ideas with Indian and Persian ones. Arabic numerals are derived from Indian ones, in fact. So you see a fertile early period of wealth (think the court of Harun al Raschid), poetry (think Omar Khayyam) and invention (think Algebra etc). Notice how much of the sky was named by early Arab/Moslem scientists. And how relaxed Omar Khayyam makes life sound: "A jug of wine, a loaf of bread - and thou!" And then the fundamentalist dogmas are imposed by scholars like Al-Ghazali. And with it, the economics of Islam also gradually deteriorate.
This is too sweeping and neat to be more than a high altitude view. There's a lot of stuff going on alongside, such as control of trade routes, Golden Hordes etc. But I think the industrial revolution, which first emerged in Britain, and which brings modern economies into being, is not especially the result of the peculiar benevolence of the UK's agriculture and climate. At least, I have never heard anyone praise the drizzle that way before. It has more to do with an open intellectual model founded on a stable system of governance. And that system of governance was increasingly secular.
For me, freedom of religion and freedom from religion are intrinsic parts of the success of the West.
On the other hand, it seems that various interpretations of Islam are at odds with the kind of peace and stability required to generate wealth. Heck, Islamist terrorism seems to glory in destroying business assets. How many Westerners are going to visit the beaches of Tunisia and Egypt after the recent attacks? Even at the level of peaceful economic management, Islamic sharia has a lot to say about how an economy is run. Just think of the denial of interest in banking, to begin with.
The fundamental difference between Islam and Christianity is that the latter is a religion and the former is a system of politics, law and religion. Christianity can play a submissive role. Islam cannot. It's very name demands it. We wonder why Moslems are always seeking to impose sharia on the rest of us. It's because sharia is a part of what Islam is. It is permanent, God-made, perfect law. If for no other reason, Moslems will cut off heads because of this. And Christians will not. Canon law is applied to ecclesiastical matters. Secular law is free-standing. And because it is man-made, it can change.
So in the experience of European and Islamic history, I believe the religious realities are not independent of the outcomes. Islam is an important explanation of its own destiny. Christianity also, but more in its marginalisation than its contribution to modernity.
| 
