
Kaleb K. answered 11/30/21
PhD Candidate with a field focus on World History
Short answer: Both societies were dominated by male authorities, but Roman society allowed relatively much greater opportunities for women than in Greece, depending on what you mean by Greece.
I think it's important to be clear on what we mean when we say Greece in the ancient world. There were hundreds of individual Greek city-states (poleis in Greek) across the Mediterranean and the Black Sea. Therefore, it is hard to make any sweeping claims about Greek culture. But, usually these comparisons are made between Rome and Classical Athens, in which case it is much easier to show the differences. Likewise, Rome was a vast, cosmopolitain empire that contained many different cultures. Again, there will be many differences in how women were treated across the empire. But some generalizations can be made.
Here are two key differences that I think clarify how Rome and Athens at their respective heights treated women. In Rome, free women (not slaves) were considered citizens of the empire and benefitted from its military protection and were granted some limited rights, though they could not vote and were legally under the authority of fathers, husbands, or some other male relative. In Ancient Athens, women were not citizens and had no official role in political life. Roman women were in charge of the household, manging servants and slaves and exercised broad domestic authority. Athenian women were segregated even in their own homes. If a male vistor came to an Athenian home, women were expeted to close themselves off in a special part of the house--the gynaikeion, or "the women's part of the house--while the men kept company in the rest of the house, called the andron, or "the men's part of the house."
There are limitless qualifications we could make about this question, but in general, both were restricitve patriarchal cultures, though the Roman Empire offered much more personal and political freedoms than in Ancient Greece.