"Advanced" is a subjective term. Can you clarify what you mean?

According to Ian Morris' Why the West Rules For Now, the East (defined as materiel cultures more or less descended from those founded around the Yellow and Yangtze rivers) passed the West (all those materiel cultures descended roughly from the first domestication of wheat) around the late 6th century and was passed again somewhere in the 16th 18th century. That's from memory. Give me a few hours, I'll get home from work and edit with more details of his argument.

EDIT: OK, I'm back. Dr. Morris is a distinguished English archaeologist who has worked both in the field and at universities such as Stanford and Chicago. Unlike many modern historians who are obsessed with the atomical, Morris wants to understand and write about the "shape" of history. His 2010 book attempts this by constructing an index of social development. What does social development mean? According to Morris, "By this I basically mean societies’ abilities to get things done—to shape their physical, economic, social, and intellectual environments to their own ends." His goal is to explain why it was the West that came to dominate social development in the recent past. I'll quote him at greater length.

I will try to show that East and West have gone through the same stages of social development in the last fifteen thousand years, in the same order, because they have been peopled by the same kinds of human beings, who generate the same kinds of history. But I will also try to show that they have not done so at the same times or at the same speed. I will conclude that biology and sociology explain the global similarities while geography explains the regional differences. And in that sense, it is geography that explains why the West rules.

But let's not mistake him.

Geographical differences do have long-term effects, but these are never locked in, and what counts as a geographical advantage at one stage of social development may be irrelevant or a positive disadvantage at another. We might say that while geography drives social development, social development determines what geography means. It is a two-way street.

He is proposing a dialectic. Not a Marxian one of social classes, but one between (as he would say) chaps and maps.

EDIT 2: How exactly does one measure "social development" anyway? The details are complicated, but I can give an overview. Morris takes his lead from the UN and their various indexes. He tries to isolate specific societal traits that he can use to create his index. I'll let him explain some of the difficulty there.

The index must measure as few dimensions of society as possible (keep it simple) while still capturing the main features of social development as defined above (don’t make it too simple). Each dimension of society that we measure should satisfy six rather obvious criteria. First, it must be relevant: that is, it must tell us something about social development. Second, it must be culture-independent: we might, for example, think that the quality of literature and art are useful measures of social development, but judgments in these matters are notoriously culture-bound. Third, traits must be independent of one another—if, for instance, we use the number of people in a state and the amount of wealth in that state as traits, we should not use per capita wealth as a third trait, because it is just a product of the first two traits. Fourth, traits must be adequately documented. This is a real problem when we look back thousands of years, because the available evidence varies so much. Especially in the distant past, we simply do not know much about some potentially useful traits. Fifth, traits must be reliable, meaning that experts more or less agree on what the evidence says. Sixth, traits must be convenient. This may be the least important criterion, but the harder it is to get evidence for something or the longer it takes to calculate results, the less useful that trait is.

He eventually settles on (1) energy capture (defined roughly in terms of kilocalories per day), (2) urbanism (using the largest city as a rough guide to societal organization), (3) information processing, and finally (4) war making capacity. He used the year 2000 as a benchmark, setting the highest possible score for each category at 250. Tokyo had around 26.7 million people, thus it scored the maximum 250 for the East while New York scored 157 for the West, and so on. Morris admits that this amounts to "chainsaw art" but again he's looking for the shape of it all.

EDIT 3: Back to your specific question. According Dr. Morris, the East passed the West some time in the middle of the 6th century. Why? The answer can be found in how the respective cores reacted to falling of social development in both dating from the 3rd century. In the the West, the Western Roman empire fell apart to invasions of nomads. The agricultural center in Tunisia and the old heartland of Italy was wracked with numerous wars, including Justinian's Pyrrhic conquest of the same. Justinian tried to use the wealth and power of the old center of Western civilization to reconquer the devastated lands lost to various barbarians. This was ultimately a failure.

In the East, the story went differently. The old heartland of Chinese civilization in the north around the Yellow river was overrun by nomadic invaders not so different to the Huns and others who ruined Rome. Huge numbers of people fled to the rural and backward south, including what was left of the imperial administration. The people in the south then proceeded to transform rice agriculture. The remnants of the court generally failed to control this burgeoning wealth, and it continued to grow. In the north, the barbarian rulers abandoned small scale states and coalesced into a new militarily powerful dynasty, the Sui. The Sui invaded the south, and quickly captured its new wealth. This new synthesis led the East to climb back up in social development while the the West continued to languish.

This is already a wall of text. If you'd like, I can discuss his explanation for the West retaking the lead in the mid to late 18th century in another post.