Catholicism saved Western Europe from complete barbarism after the fall of Rome. This is actually true. The Church as organizing unit was in fact extraordinarily useful in the development of modern techniques for centralizing power, enabling the formation of the modern nation-state.
(China had independently developed many of these tools earlier, but they didn't push it as far. Probably partly because they didn't have any significant rivals to make them need to--when the Mongols descended upon China, they assimilated, and in a few generations we had Kublai Khan and his artful luxuries.)
The modern state in turn allowed countries/kings to focus their aggregate power more tightly, which allowed them to gather more power, which generally encouraged prosperity, which encouraged learning and other such luxuries, which encouraged open thought.
For that matter, the Inquisitions invented indexing. To keep track of past testimony. It was at the time a terrifying power. Nobody expected anyone to know for sure what they said five years ago, even if someone had written it down at the time.
Like the Aztec state religion, which was reinvented by one man to hold together an empire of more numerous subjugate peoples, the Church and its offspring was a powerful ideological and logistical tool.
This is true. Constantine's systematic establishment of Christianity as the new imperial cult in the midst of decline and loss of confidence in the Empire was actually a good move. Anyone who blames the Dark Ages on the Church is willfully ignorant of both late Rome and the Byzantines. (Religion caused much political upset within Constantinople, which is in some ways one of the most religious cities in history, but it most certainly did not undermine the empire.)
There are also philosophical elements in the doctrine itself that encourage the concentration of power in singular authorities, and expansion without limit, and the organization of the conceptual universe into absolute systems, which last does seem to have laid major groundwork for modern scientific inquiry. All three of these probably encouraged European development in an advantageous direction.
But to infer from this an intrinsic superiority in anything but raw power is, I think, skipping anything that might be called intervening logic.
Edit: @UHM and possibly others: China was an empire. The unification of what were quite frequently divided states with separate dialects and local customs under one throne, and the tribute of the satellite states, pretty strongly qualify the Middle Kingdom for most of its history. Had Rome persisted to the present day it would probably present a similar cultural profile, in terms of a Roman identity. Look at Roman Britain.
On a totally unrelated note, moveable type is much less obviously practical in a writing system with thousands of ideograms than in a system with twenty-odd phonetic signifiers. You'd spend longer finding the right print-block than writing the damn character and three more besides, and the result would be far less attractive. There might also be hundreds of it, but it's hard to grasp the advantage of mass printing until you've seen it over time. Besides, literacy was an art. People who didn't have time or skill to do it properly shouldn't be doing it at all. Calling China anything but vertically structured would be pretense.