As an exercise, does "give unto Ceaser ..." explain why say, the Chinese succumbed (Unequal Treaties, Opium Wars)?
China had in a sense the opposite problem from the Islamic world, no concept of a legitimate institution independent of the central government.
Whatever it was that made the British beat the Chinese back then or makes China ascend so quickly today as to leave All of Europe combined let alone the UK in its dust,
Careful, 20 years does not a historical trend make. The only reason it appears this way is that a European bubble is in the process of collapsing, whereas China's hasn't yet.
I'm bolding this just in case you aren't familiar with Ibn Khaldun's theory to emphasise how important this is. I would argue that it is basically correct.
At this point I ask my fellow rationalists to consider. If this was the case, what might decline of 'asabiya look like in modern secular societies if it was happening?
If only people commenting on upheavals in the Middle Eastern world actually knew anything about the Middle East, they might actually make usable predictions. Not that punditry is about predictions anyway.