This fall of Rome comparison is old and very tired. No one really knows why Rome fell and if you ask 10 historians you will get 10 different answers. How did Egypt fall, how did the Soviet Union fall, how did the British Empire fall?
Those ten historians may differ on the finer points but all will agree on a common element that lead to the downfall of the societies you mentioned: internal corruption and political greed.
All of which are, to some degree, correct. There's rarely a single cause for great historical events -- if we can even properly call a centuries-long process an "event."
About all we can really say is that the Roman Empire fell apart from within at the same time it was being defeated militarily from without. Dr. Fears is correct when he points out the bloat and inefficiency within Roman institutions.
IMHO, such bloat and inefficiency occurs when a government tries to make up for the decay of individual virtue. As John Adams said about our own Constitution:
"We have no government armed in power capable of contending with human passions unbridled by morality and religion. Our Constitution was made only for a religious and moral people. It is wholly inadequate for the government of any other."
The Roman citizenry had to a large extent lost the civic virtues -- a sense of duty to Rome -- and were instead focused on their own affairs and gain. There's nothing intrinsically wrong with the latter, but if it's not balanced by a sense of responsibility to the larger group it becomes decadence. That is the real lesson of Rome, and we can see it at work here.
A lot of people who bring up the topic are talking more about the present than about Roman days. Many of them are looking for some kind of answer or law to explain why societies decline and fall. Some of what they come up with is wrong or has more to do with our own condition than with anything that happened in Rome.
But the "other side" that doesn't want to discuss the question makes similar mistakes: a Boston Globe editorial of a few years back said that it had been proven that lead in Roman crockery brought the empire down, so all talk of decadence was pointless. I hope we can all agree that that's not an especially useful attitude.
Rufus Fears teaches at Oklahoma University, and has recorded lecture series for the Teaching Company. They're interesting and useful, and Fears is certainly conservative, but he's more of a preacher or popularizer than a detail man. Anyone who wants to know more about Greece or Rome, or Winston Churchill or the history of freedom might look into his lectures, though they're certainly not the last word about such topics.
The problem with discussions about why empires rise and fall is that objective and subjective factors are so entwined. Bring in morality and things get yet more complicated. The British empire faced serious anti-imperial sentiment in the 20th century. But the objective fact of two world wars probably did as much to doom the empire as anything else. And if we ask ourselves whether the empire was a good or a bad thing at this or that point in history we get into quite a discussion.