The Greek/Roman art included pillars, realistic glorified people who were proportional, meanwhile the golden ratio did not apply at all in the Middle ages. There is nothing similar in these two societies except that art was created by artisans. The government was also none in the same.
In the barbaric society, also known as the Germanic tribes, they had small bands of warriors led by lord, unwritten laws, traditions, and family ties, also ruling a large territory was impossible that made up their government. On the other hand, Rome had a large public government, had unified laws and ruled vast territory. Which means that all the rumors that vikings are barbaric is true!
Civ students have vast knowledge in Greek and Roman lifestyle and now they also know about the Germanic tribes. We can conclude there is nothing that these two societies share in common in terms of government and art. Although the Medieval was based on the Roman Heritage, Catholic Church and Germanic Tribes, that is the one of the only things that can link these two societies.