One of the most interesting discussions I've come across recently is the diavlog between Rod Dreher, author and journalist with the Dallas Morning News, and Cullen Murphy, author of Are We Rome?, found here. The periodic comparisons of our ongoing American cultural decline to that of ancient Rome always makes for a good debate. Personally, I believe strongly and unequivocally that...well, it is...and then it isn't. Similarities abound, certainly, but these are sometimes simplistic and superficial, and there is obviously much that is dissimilar between the course taken by the two empires.
I have some major reservations with the hypothesis. First, Rome really didn't fall, as such--or at least not the way generally thought, or when generally thought. Certainly there were times when the barbarians were literally at the gates, so to speak. But there was never a time when a Roman citizen of southern Gaul, for example, would stop and say, "my, haven't things been crappy since Rome fell." From my readings, I find no sense of such a sudden change. Societies changed and evolved, and in many ways declined, but the transformation was slow and often imperceptible and life went on.
Also, the end of Rome is either tagged at 410 AD (Visigoths), 455 AD (Vandals), or 476 AD (death of Romulus Augustus). But by the time Rome "fell," it had already been superseded (and eclipsed) by the New Rome (Constantinople.) These Romans of the East thought of themselves as exactly that, the "Romaioi." They would have been puzzled if anyone had addressed them as a Byzantine. And not only that, but this New Rome-for centuries, the marvel of civilization-continued on until 1453. So, even if one were to buy into the whole America=Rome theory, the date used for comparison is about 1,000 years shy of the final fall. The Roman experience is instructive for any culture, in any time, but one should be cautious in drawing too many comparisons.
That said, comparisons are easy to come by, even with the Eastern Romans. I am currently reading Michael Arnold's Against the Fall of Night, a 1975 fictional account of the Comnenian Revival of 12th-century Constantinople. In many ways, the era (1080-1204) marked the very pinnacle of Byzantine civilization. But behind the glitter and pageantry, the rot had already set in, their projected power something of a deceptive facade. For centuries, Constantinople had maintained a defensive posture--simply trying to maintain its borders, or what had once been theirs. This changed with the latter Comneni, who were aggressive militarily, which quickly exacerbated the underlying weakness of the empire. But even after the catastrophe of 1204, the Byzantines came back and held on for another 200 years.
American culture may have even more in common with Rome than we realize. But these things work out over extremely long periods of time. Even if true, we have a bit of a run yet, and I doubt if things will play out exactly as the doomsayers often predict.