well, rome kinda had a decline starting with bad emperors, and ending due to bad timing with the invading goths, huns, etc.
whereas byzantium slowly wore itself down financially and politically due to internal squabbles less than bad emperors (though these of course weren't uncommon, as in any state/country/empire/nation) and trying to overstretch themselves. of course the crusaders sacking of constantinople was a huge loss.
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