one half showing three girls wearing casual clothing walking down a street in Iran in the 1960s, the other half was showing three girls wearing burqa walking down a street in Iran last year.
I'm by no means an expert in the domestic laws of Iran, but these kinds of photos are a relatively common comparison that's made for many Islamic countries, often made with an explicitly political message in mind. Here's one such example from Egypt http://www.frontpagemag.com/fpm/48901/how-veil-conquered-cairo-university-jamie-glazov which purports to demonstrate by the rates of veiling in class photos at Cairo university that "Radical Islam has taken over even the minds of educated women in the Muslim world."
As a preface, just so we're clear on the terminology we're using, have a look at this BBC guide on Islamic women's headwear and dress. "Hijab" and "veil" are probably the widest catch-all terms, as hijab can refer to both the style of head-scarf in the image in the article as well, as the article notes, the general practice of covering up. I'll try to make the sense I'm using that term in clear if I use it below.
There's a few things that are worth commenting on.
Yes, after the Islamic Revolution in Iran in 1979 it became compulsory, and remains so to this day, for women to wear a hijab in public. The wearing of a "burqa" was not made compulsory in the revolution and to my knowledge has never been common in Iran. Nor is the Niqab particularly common in Iran. Styles like the chadoor have been more common, for instance as worn by Masoumeh Ebtekar who was the spokesman for the the US embassy hostage takers in 1979 and is today a vice president of Iran. As a quick answer on driving, as far as I'm aware Saudi Arabia is the only muslim country that has carried out a ban on women driving cars, and it's certainly allowed in Iran today.
This is in contrast with laws under Reza Shah, who banned veiling as part of a program of secularization/modernization which was, in that instance, walked back by his son (Mohammed Reza Pahlavi - "The Shah"). Nor was this limited to women, as men were forced to westernize their dress habits as well. There's a rather amusing first hand account of this in one of my favorite books, The Road to Oxiana, but I digress. I have to admit to being on shaky grounds about the extent and efficacy of these programs in terms of my own knowledge so I won't go into their effects or effectiveness.
Nonetheless, whether it's in Iran, or Egypt, Afghanistan, or anywhere else in the Islamic world, these kinds of photos from the 1960s of women not wearing a hijab are often of an urban elite, and taken at a period when state-enforced secularization was arguably at its peak through movements like Pan-Arab Nationalism, and before the international rise to prominence of political Islamism as an elite movement in many of these countries. So if we were to look at rural communities the picture would be very different. And moreover you be able to reproduce these kinds of imagines in countries that had no Islamic Revolution or laws mandating the veil but simply given the passage of time and "Islamic revival" of the past 50ish years. Even in countries that have maintained, to some extent, whether officially or by custom, policies of secularization and anti-veiling, like Turkey, this kind of thing is a significant cultural issue.
Insofar as the hijab can be a genuinely desired expression of women's religiosity, it's worth considering in the case of the photos from Cairo whether the more "equal" photo isn't the one where women wear a mix head coverings or no coverings, insofar as many of these countries in the 1960s would have excluded devout women who choose to wear the veil from these elite institutions, either by policy or by norms. The case of Iran is obviously quite different in that women are forced to wear this kind of clothing who otherwise might not.
I think with all of that in mind, and again with the caveat that I am not a social anthropologist or particularly well-read in women's studies in the Islamic world, but it's also worth bearing in mind there are authors who write persuasively that issues like veiling in the Muslim world can be more about Western norms and needs to justify intrusion into Islamic societies than any kind of deep-felt concern for the needs and equality of those women.