I'm going to be deconstructionist and question a lot of the terms used in this question.
First, "Eastern" and "Western" Europe: As I wrote here. The idea of Europe being divided into a Western and Eastern half, each of which share internal commonalties and are distinct from each other, is largely a concept of the 20th century and is not terribly useful for historic purposes. To assume that Bulgaria and Lithuania constitute an "Eastern" idea separate from a "Western" France and Denmark is to think ahistorically: in the medieval period, Denmark and the Baltic part of Lithuania would have shared more similarities with each other than either area would have with those other examples (the King of Denmark was even Duke of Estonia for a century and a half). Central Europe gets even more complicated. Is Prague the "East"? Berlin the "West"?
"Development": specifically in terms of "was life better"? This is much trickier than it seems. We simply don't have substantial economic or social statistics for entire countries until the 19th century at the very earliest, so anything like literacy or average life expectancy, to say nothing of average income or GDP per capita that statistic that can mislead as much as enlighten.
Why do I say this about GDP per capita? Well, because even if we are able to make reasonable estimates between regions in the premodern period, the simple fact of the matter is that until the 19th century, for basically all of Europe we are talking about societies that are overwhelmingly agricultural and rural, and that lived very close to subsistence levels, with periodic famines and Even in the 19th century, the 1840s saw widespread malnutrition and famine conditions across Western Europe, with mass starvation and emigration in Ireland being the worst manifestation. So even if, say, the Low Countries in the 16th century saw more populous and richer cities than, say, Ukraine, that's not necessarily reflective of how the vast mass of the population lived. I call out GDP per capita specifically because while it can indicate that a society in aggregate is richer, that doesn't account for how that wealth is distributed. French aristocrats could be far wealthier than their Polish associates in Ukraine, with the mass of peasants living similarly, and the GDP per capita could potentially show France as having the higher GDP per capita.
So probably your best bets for looking at where different geographic regions began developing at different rates is in the 19th century with industrialization and new agricultural practices, but here I'll defer to Kenneth Pomeranz's The Great Divergence, which I will leave to someone else to do greater justice to, since I am only familiar with it in summary.