As far as I know, the Byzantine Empire was, to put it overly simply, rich and under one ruler, as Western Europe was poor and a collection of different states and monarchies. What was the factors that led to their different evolution?
I would push back against the idea that the Byzantines were necessarily more powerful than Western Europe, at least in the eighth and ninth centuries the Byzantines were struggling in many regards. In 751 they had lost the Exarchate to the Lombards and in 812 were forced to recognize Charlemagne's title as emperor. This was all part of a treaty between the Franks and the Byzantines. As to your larger question the factors are much the same as any two states. It has to do with different culture, politics, and I think most importantly for the Byzantines, neighbors. The Byzantines spend a lot of time dealing with Muslim attacks whereas the West did not. Not saying that that is the reason, but something to keep in mind.