The early Medieval period is often remembered as a time of chaos, poverty, stagnation and great devastation. While the extent of these claims are debatable, no one can really doubt Byzantium's efforts in consolidation, nor its achievements during Europe's supposed dark ages - it was the direct continuation of the Roman Empire, that more or less successfully carried on its identity from antiquity to the Middle Ages, without the kind of discontinuation what we observed in the West.
Suppose their Western counterpart managed to withstand the test of time as well - how would we see it transform into its medieval version without the grand theme of spectacular fall and eventual recovery as it was the case with the Eastern Roman Empire?