What characteristic did the byzantine empire share with western europe

Unlike the Byzantine Empire there was no single entity that could be called 'Western Europe'.

Commonalities:

However, there was one significant common trait among them. Both were seen as Christian lands where the Church held considerable power.

Both the cultures were extremely autocratic and theocratic in nature. The royal families held political power, while the church had religious influence among the people.

The society also had a fixed hierarchy the aristocrats at the top, followed by business people and soldiers and eventually the serfs who worked on the lands of the gentry.