The Western Roman Empire fell in 476, but the fall did not lead to the end of Roman influence in Europe; under the barbarian rulers, the Roman culture continued to thrive. The Eastern Roman Empire survived till 1453, but soon after it fell, all trace of its culture was eradicated. The culture of the Western Roman Empire survived the barbarian takeover, because the barbarians were devoted to the Roman way of life; the Eastern Roman Empire, on the other hand, was vanquished not by barbarians but by an organized religion—the religion of Islam. The Ottoman Turks (along with the Persians and Arabs), who defeated the Eastern Roman Empire, established an Islamic kingdom, which, in some form, continues till this day. In the sense of culture, the Western Roman Empire never fell, whereas the Eastern Roman Empire’s fall was total.
PS: In volume five of his History of The Decline And Fall Of The Roman Empire, Edward Gibbon says that the Latin Crusaders and the Ottoman Turks led to a “double fall” of the Eastern Roman Empire.