I was wondering what was the extent of the people who fled to the Eastern portion of the Empire following the West's fall in 476A.D.
Aside from well-known refuges such as Venice, did the majority of the commoners choose to stay? Were there any major incentives to stay or leave?
As for the aristocracy, did they lose their wealth to the Germanic people? If they did flee to the east, is there any connection between them and the aristocracy of the Byzantine empire? If they stayed in the western kingdoms, what became of them by the medieval times?
The quick answer is there were probably some but very few.
The simplest reason is that no one could really afford to.
Regular people living in the provinces would have actually done a bit better under Barbarian rule than they did under the very late Western empire. The only thing they really had seen of the empire for a few generations leading up to its collapse were officials who either wanted to draft them or collect taxes.
Also, the Western empire lost territory gradually in what was originally, nominally at least, a refugee resettlement program for various Germanic and a few other Barbarian tribes, in exchange for military service. This was fine because a few European provinces like Gaul and Hispania were sparsely populated, and even more so after the Antonine Plague and the Crisis of the 3rd Century had done their thing. Throughout the 4th century or so, the trickle of new faces within the empire became a raging torrent. These tribes became increasingly more independent, and eventually their soldiers became pre-packaged armies, with their own corps of officers and even other hired Barbarians, but nominally they (mostly) served the Roman Empire, or at least served some political faction within it that served their best interests. From what I can gather from all this is that although the Barbarians were still ethnically and decreasingly culturally apart from the common Romans, they were very much settled in by 476. They also had their own aristocracy and landowning class, which provided the same "employment" (read basically serfdom) that Roman landlords had. By the 430s, the Vandals had decided they quite liked North Africa and wanted to play for keeps, laying seige to big cities like Hippo Regia and eventually Carthage. In those instances I'm sure people would have definitely fled east if they could have, but most of the time people didn't know Barbarians were coming to lay seige until they were already almost there. This was true across the empire but especially true with Carthage.
Also, the East was in pretty sorry shape in 476 as well, largely because of a massive and botched attempt to retake Carthage, but would gradually recover over the next few decades.
I have more to talk about tomorrow, a LOT more, so I'll edit this answer asap. If you see this before then, I hope this somewhat answers your questions. But the street-level perspective is incredibly hard to research as documentation of life then is sparse and unreliable, and almost as hard to get one's head around.