This is a hard question to answer, because these civilizations that you are speaking of are extremely broad. For example, Hellenistic Greece spans the Middle East, North Africa, and Europe. In light of this, there is no monolithic answer that can be given. Good answers and methodologies will always include geographical variations. With this stated, we can only give general statements.
I would say that the status of women, as time progressed, grew (a bit) to be more equal to men. The status of women in classical Greece was very low. Their place was in the home and they had little rights. Some scholars even question whether they were allowed to go to the theater. So, it is hard to imagine that their status would decrease.
When it comes to the Hellenistic era, there is some evidence that the role and status of women increased. Let me point to two of them. First, in Ptolemaic Egypt, women seemed to have more power and they could be rulers. Second, with interaction with other cultures, who viewed women a bit higher, such as Rome, there might have been improvement.
In conclusion, there was probably a slighter higher status of women, but no big step forward.