Perusing some old threads here, I noticed a lot of speculation regarding when, exactly, the old Roman Empire morphed into Rhomania/Byzantium and exactly how much continuity and legitimacy it really had in later periods. Gibbon was obviously somewhat prejudiced in his view of the later Empire, though most Western Europeans were at the time. Yet, even Gibbon understood the epic magnitude of the fall of Rome. It was not a single event, it defies any attempt to accurately date it. In some ways, Rome never fell.
Majorian was the last Emperor of the West of any real note. He reestablished Imperial supremacy in parts of Gaul and Spain, he still had a name that reflected the old practice of tria nomina. But it is telling that even Western coinage in his period looked remarkably Byzantine-esque. The votive crowns of the later Visigothic period in Spain seem like something that, save the designation of "Rex," could have come straight from the Byzantine Court. There is at least some possibility that it actually did. The Visigoths were building cities and churches off Roman designs. Even Frankish coinage, such that existed, continued to look remarkably Byzantine-esque for a long time.
Byzantine culture WAS Roman culture. It was simply extinguished in the West after the Arabs had basically cutoff the Eastern Empire from the remnants in the West. As command of the sea was lost and far-flung ports in Africa, Spain and Italy drifted out the Imperial sphere, contact with the the Gallo-Romans, Northern Italians and Hispano-Romans was lost, the latter due greatly to the depredations of the Arabs.
From a linguistic perspective Greek and Latin languages were co-dominant in the old Empire. But the Latin drifted out of the Imperial sphere along with the Latin territories, so slowly that it was probably difficult for the common folk to even realize it was happening.
In other words, I argue that there was a break, but the break occurred in the West and not the East. If the Arabs had not shown up, I suspect the West would have evolved along similar lines as the East, even if many of those territories were ruled by Germanic dynasties. There would have been much more cultural influence exerted by Rhomania.
Rome was very similar to China, in that it was a bureaucratic Empire that created, for a time, a unified meta-culture. But unlike China, at the center of that meta-culture was the Mediterranean Sea, a vulnerable center. The Vandals demonstrated how quickly piracy could ruin the Roman economy, so dependent on that vulnerable center for survival. Belisarius's lightning campaign fixed that problem for awhile, but the Arabs wrecked Roman control of the Mediterranean forever, and with that, the various regions drifted out of the Roman cultural sphere, so slowly that civilization hardly noticed, day-by-day.
The transitional period from 602 - 751, from the death of Maurice to the final fall of Ravenna, marked the end of Roman control in the West and with it, the final opportunity to fulfill Justinian's dream. Rhomania was the legitimate successor, with full continuity with the ancient Roman State, but it was no longer the Roman Empire in its proper sense: a Mediterranean-spanning meta-culture. There would be no restoration as happened in China, and so each island of Roman culture went its own way. Rhomania was, simply, the first among equals and the only state that could really trace an unbroken tradition all the way back to the beginning.