When the Roman Empire collapsed in 476 AD/CE, much of the Italian peninsula-(including Rome), as well as many countries to the North and West of Italy proper, fell into "The Dark Ages". Countries, such as Austria, Southern and Western Germany, parts of Switzerland, much of France and the near entirety of England, as well as the majority of Italy, fell into a cultural and political decline until the beginning of the 2nd millennium AD/CE-(the traditional starting point of the Late Middle Ages). Although the Roman Papacy was still quite powerful throughout the Middle Ages, much of its power and influence was regional and primarily confined to Italy proper, as well as to the historically less sophisticated and economically underdeveloped lands to the North and West of Italy.
It was a different historical reality for the Eastern half of the Roman Empire. Although it was actually the Emperor Diocletian who officially separated the Roman Empire into Western and Eastern zones, it was essentially the Emperor Constantine who literally relocated the Administrative capitals of the Roman Empire to Milan in Northern Italy, as well as to the centuries old Northern Greek city of Byzantium, which he renamed to, "Constantinople" around 306 AD/CE. It was Constantinople, that would follow in Rome's imperial footsteps........ towards the East.
The commercial and geopolitical strength of Constantinople was important, due to its close proximity to Asia, especially the famed Silk Route-(which begins in Constantinople, from a European perspective), as well as having close access to the Mediterranean and Black Sea regions. Although the Byzantine Empire faced invasions from Slavs, Vikings, Goths, Arabs, Crusaders and ultimately, the Ottoman Turks, it was an extremely powerful state which had the capacity to counter such invasions over an 1100 year period-(with the notable exceptions of the Crusaders, as well as the Ottoman Turks).
Comparatively speaking, Byzantine Constantinople absolutely dwarfed Early Medieval Rome in terms of its political power, economic and commercial wealth, cultural refinement, religious influence and historical longevity. Early Medieval Rome, as well as its former Western colonies, were in the distant shadow of Constantinople and the greater Medieval East. Even with the short lived accomplishments of the Carolingian Renaissance ushered in by Charlemagne in Aachen, Germany during the late 700's, the balance of power during the Early Middle Ages.......was in the East and Constantinople, was its Center Point.