It is true that up to the 18th century, the Empires on the eastern part of the Eurasian landmass were just as successful, if not more successful, than the smaller states on the Western extremity (depending, of course, on whatever measure of success is being used).

Most modern economic development is attributable to the Industrial Revolution, which occurred first in Europe. There are a number of theories as to why Europe industrialized first, including one that puts it up to pure happenstance, but the most popular is an idea called Institutional Development Theory. This theory postulates that the small western european countries in constant competition with each other were pushed to maximize efficiency as well as entrepreneurship, eventually culminating in industrialization.

Of course, industrialization itself was an uneven process: the Netherlands after 1600 and the western and central British Isles were early movers, with the urbanized parts of Eastern France and Western Germany following closely. Other parts of Europe, including parts which had been traditional economic centers (like Italy) were late industrializers. Just as one (very cursory) example, the British Isles were historically less populous than the rest of Europe, and this placed a significant upward pressure on wages. This means that English workers could enjoy a higher standard of living, while English employers were always on the lookout on ways to increase efficiency and keep their costs down. There are also a number of other factors though, like the presence of coal on the isles, England's seafaring heritage facilitating the foundation of colonies where raw materials could be obtained, and the presence of a relatively weak monarchy that had to rely on a consensus-based governmental system, fostering consistent and fair rule of law. Different authors will stress different variables in the case of Britain as with other economies, but I don't think it's accurate to emphasize one over the other. All culminated to make the industrial revolution, and economic divergence, happen.

The first to put forth this idea was Paul David, in his 1994 article "Why are institutions the Carriers of History?" and the idea has been reaffirmed multiple times, notably by Douglas North in 2005 ("Understanding the Process of Economic Change") and Avner Greif in 2006 ( "Institutions and the path to the Modern Economy").

You might also be interested in the ideas put forth in these texts:

B. Gupta and D. Ma, “Europe in an Asian mirror: the great divergence”

J.L. Rosenthal, R.B. Wong, "Before and beyond divergence. The politics of economic change in China and Europe"

S. Broadberry and K. O’Rourke (eds.), "The Cambridge Economic History of Europe"

S. Broadberry, "British Economic Growth 1270-1870" (just to get an idea of what the prerequisites for industrialization are)

I myself participated in some threads on this topic which you might be interested in:

Why did Western Europe develop at a faster pace technologically than other nations in Europe during the renaissance despite being geographically further from Greece and Italy than, say, Hungary.

And,

Why did the Industrial Revolution begin in the UK and not elsewhere? I have seen several theories, including colonialism, natural resources, Protestantism, capitalism and the rule of law. Is there any historical consensus on this?

As always more can be said but u/profrhodes has a post that has since been added to the faq that addresses this very question: https://www.reddit.com/r/AskHistorians/comments/1pzf28/why_did_european_powers_in_particular_start/cd7n7j1/?context=3