Both periods are similarly described as "dark ages" because during both periods literacy was almost lost and writing almost disappeared.
The Mycenian palace system needed many people knowing how to read, write and use numbers to function properly. With the implosion of this world, people didn't need to read and write that much and reverted to the oral tradition. No more of these great written inventories of all things, from slaves to war chariots, found in the remains of mycenian palaces.
In the 8th century BC, Homer still followed the oral tradition. The great story teller never wrote his story.
The same happened with the implosion of the Roman world. Literacy became unnecessary, to the extant that the barbarian kings that followed the roman emperors, being as illiterate as their subjects, used templates to sign their names. In this case, literacy was preserved by the church.