Pahlavi was better even though that isn't saying much.
I've done a lot of research on women in Iran, and Khomeini is one of the worst things that ever happened to them. He was pretty much a monster.
Indeed - Pahlavi's support for and provision of Women's Rights is one of the reasons as to why so many uneducated and delusional folk joined the Islamic Revolution. The Pahlavi dynasty provided for, inter alia, the expansion of the electoral law to provide for full universal suffrage and widespread educational opportunities were implemented for women (not to forget the abolition of the veil).
Yes, although many of the people that took part in the Islamic Revolution were young women that were turned off by what they thought were vacuous "western" values. They thought that the Shah focused too much on forced cultural liberation while ignoring basic needs like clean water and decent housing. They thought they could be anti-western and anti-imperialist while still being pro feminist, and Khomeini was quick to accept them into his ranks because it made the movement much stronger. When Khomeini reversed policy and betrayed women in the early 80s, there was a lot of protests from the same women that supported him in the revolution. And he basically saw to it that they were murdered, tortured, and raped for their efforts.