Which conflict was harmful to the Byzantine Empire but not to the Roman Empire?
This is a tricky question since the Byzantines considered themselves inheritors and the continuation of the Roman Empire, but the struggle that ultimately led to their downfall was that against the Seljuk Turks. Following the Battle of Manzikert, they would lose Asia Minor except for its westernmost coast which took away a massive source of grain as well as more than half of the manpower they could have used to rebuild their armies. The worst part was that it could have been avoided if the ruling powers in Constantinople wisely dealt with Alp Arslan (leader of the Seljuk Turks) and honored the agreement of ransom and tribute brokered by Romanus Diogenes (the Byzantine basileus, or emperor, at the time who lost the battle). When they didn't, it provided the Turks with the excuse they needed to sweep into Asia Minor, forcing the already emaciated borders of the Byzantine empire further back from which it would never recover.
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