Can you see how 'open relationships' would be more advantageous to women?

Not really. Even if both people agree to see others she would still end up on the losing end, at least in the eyes of others. She's pathetic for allowing her man to sleep around and she's a whore for sleeping around herself. They're both adults who can make their own decisions but like many similar sexual situations, it would make the woman look cheap and the man look like a stud.