How did life western europe deteriorate compared to life in the byzantine empire after the fall of the roman empire?

The Byzantine Empire and Western Europe originally were part of the Roman Empire, but by the Middle Ages, they were vastly different, though they shared common traits, but by the 300s, the Byzantine Empire had far surpassed Western Europe in trade and economics and political unity, while both empires were having arguments over religion. ~ hope this helps ! (:

the american gained the respect of other foreign nations