However, if you read Why the West Rules for Now (which serves as a pretty good East and West world history), the author basically says near the beginning that of course geography played a big role in where early civilization started.
But, to the central question of the book, that doesn't begin to explain why China had to pay homage to Britain, rather than the other way around.
If I understand correctly, China could have ruled the world at least twice.
First, around 1100, China was starting in on an industrial revolution. They peaked at tens of thousands of tons of iron produced each year. Then the mandarins noticed that some commoners were getting rich, which was contrary to the proper order, and the government shut down the iron industry, and the whole thing stopped. But they could have had at least the beginnings of the industrial revolution five centuries before England. (Source: The Victory of Reason, by Rodney Stark.)
Second, China had fleets that dominated at least the Far East, and could have dominated the Indian Ocean. But shortly after 1434, the Chinese emperor decreed an end to the voyages of their great fleet. (Source: 1421 and 1434, by Gavin Menzies.)
Underpinning the book I referenced, the author Ian Morris put together a very detailed attempt to quantify the overall level of civilization [1].
Certainly after the Fall of Rome, the West declined precipitously. I've been reading a bit about that period in Europe recently and the extent of the decline is really quite staggering. It's uneven to be sure as areas of the Middle East, for example, didn't really fall as far.
In any case, China was arguably more advanced than Europe for a significant period and certainly didn't trail significantly until the industrial revolution in the West. (And the industrial revolution(s) pretty much swamped everything that came before.)
ADDED: The book is pretty light on the why behind the West's relative success but there's some speculation, as I recall, around centralized government and general conservatism caused China to miss out.
In Jared Diamond's "guns, germs and steel" an explanation given is that in China, some monarchs simply decided to abandon ocean faring ships, and so China didn't have them for a long time. The same couldn't happen in Europe, because there were so many small competing countries.
However, if you read Why the West Rules for Now (which serves as a pretty good East and West world history), the author basically says near the beginning that of course geography played a big role in where early civilization started.
But, to the central question of the book, that doesn't begin to explain why China had to pay homage to Britain, rather than the other way around.