Geographically ERE was easier to defend. What wasn't easy to defend wasn't too valuable either: the Balkans, most of Greece (except for Thessaloniki which was valuable being a major European city of that period) and the Anatolian plateau.
This meant even a mediocre emperor or relatively small armies could defend what was really worth defending.
This might have also worked as a deterrent to some extent for the local potentates: when rebelling they needed to make considerable more efforts to really take control of the vital parts of the empire compared to a 3rd or 4th century WRE self-proclaimed emperor. Constantinople itself was a much tougher nut to crack than Rome.
However the list of rebellions and Byzantine coups shows such deterrent was not strong enough to discourage both the successful and the unsuccessful generals who attempted to grab the imperial purple.
First of all, Aspar was killed in Constantinople, far away from his troops. Belisarius was also blinded in Constantinople by Justinian I, also because he could not have his troops at hand.
Why couldn't any of those powerful generals bring their armies to Constantinople?
Because that was illegal and by marching his army on Constantinople (just like marching on Rome) one would place himself outside the law.
It was OK to do that if the emperor was unpopular and nobody else was willing to come to his defense (this is why unpopular emperors could not hind effectively behind the formidable city walls). But marching with his army on Constantinople in times of relative calm (and even some idiotic emperors still managed to remain relatively popular) was a very risky business both for the general and for his troops. The emperor would have been able to defend the city walls with the local garrison and with the help of the population while other generals would come to the rescue. And those generals would come to the rescue for the simple reason there was only one throne and too many generals. So why that thorne should belong to that rebel? (just like in the WRE where many emperors did find supporters among the other generals).
The equation was really simple: a successful coup would require an unpopular emperor (even though he might have been an otherwise military competent one, like Maurice or Nikephoros II Phokas) so nobody would feel like coming to his aid and preferably some "commando" already inside Constantinople.
Well, the opposite seems to have been true if we take a look at the Catholic kingdoms. Once it was established by law only those from the royal blood can become kings or queens and clear rules of succession existed for those of royal blood, the rivalries among the generals where capped. Competent people kept doing their best in exchange for royal favors even though they could not get the throne anymore.
Yes, having an incompetent or a too inexperienced king did damage the kingdom on occasions (sometimes leading to its demise - like the Hungarian Kingdom which only survived on paper after the battle of Mohacs 1526 or like the Balkan kingdoms facing the Ottomans in the 14th century).
However statistically the kingdoms with clear rules of succession proved more resilient. Not only because they've lasted roughly as long as the Byzantine empire (they were set up in the 8th - 11th century and lasted till nowadays), but because the same experiment ("let's see how much punishment this kingdom can absorb from its incompetent leaders and from its sworn enemies") was run on much more "samples" (several kingdoms as opposed to a single empire) and was generally successful.
While "let the best man be the emperor/king/president" sounds good, it only works in societies where the middle class is the largest section of the population. This is why it could only work in the relatively small city-states in the Ancient and Middle-Ages times and nowhere else (though those "democracies" where not exactly democratic by our standards).
This is why it didn't work in South America until the end of the 20th century and this is why it doesn't work in some parts of Asia and Africa even in the 20th century. If most of the people are relatively poor and the faster track to a better life is having a weapon in hand, "the best man" means whatever warlord or general is better at the job of eliminating his armed competitors.
And there's only one way to find that out: not by elections. By civil war.
The ERE could absorb more civil wars and coups than the ERE just because it was richer and better protected by natural obstacles than its western counterpart. For the rest, it was a mess, with every 3rd emperor on average being overthrown, blinded or killed.