There is an inequality for nuns and monks. Not for lay women.
Most Buddhist nuns you meet. in almost any Buddhist tradition, including nearly all Tibetan Buddhist nuns, have only received novice ordination and never go any futher.
That's because in most of the lineages, the full nun ordination has died out. It's only present still in a few traditions in China. So depending on the tradition you join, you may find you simply can never become a fully ordained nun, like the monks.
And some monks in some traditions are resistant to the idea of reintroducing full ordination for nuns from China, which they could do. While others are forward thinking and are strongly in favour of doing so (like the Dalai Lama) but meeting some resistance, and others are actually going ahead and doing it.
That's all because of some things in the sutras about the Buddha's reluctance to ordain nuns originally. But the Dalai Lama and others say that is due to the traditional position of women in society back then and that the reasons he was reluctant to grant ordination then simply don't apply any more in modern society.
And there are some strange rules, at least strange to us in modern times, that make a Buddhist nun, even fully ordained, however many years they are ordained for, count as "lower in rank" than a Buddhist monk, even if he has been ordained for just a single day.
The reason for all this may be because back in the Buddha's time, then a nun would be seen as a "loose woman" if she doesn't have the protection of a man, especially if also wondering as a homeless person, as many of the nuns did. By making them subservient in the monastic rules, it then made it clear to everyone that the nuns were under the protection of the monks, so respectable women. That probably helped to keep nuns much safer.
While as a lay women practitioner you don't have that at all.
You might like this book: Cave in the Snow: Tenzin Palmo's Quest for Enlightenment: Vicki Mackenzie: about one of the first Westerners to become a fully ordained Buddhist nun, she had to travel to China to do so. And she spent years in caves. And ran into many issues as a nun amongst traditional Tibetan monks. And was involved in the movement to get full ordination reintroduced into the traditions that lost them. It talks quite a bit about these issues. And BTW she is a remarkable women, might be inspiring to read about her. Lots of videos by her too.
In the Kagyu tradition, the Karmapa, most forward seeing of them all, has actually taken on the commitment to introduce full ordination to nuns, and set the process underway - which will take a while as it has to go through various stages. Gyalwang Karmapa Makes Historic Announcement on Restoring Nuns’ Ordination
Whatever the reason for those rules, they may have been necessary once, but they seem archaic in modern society. We can choose not to pay much attention to them .They really only make a difference in certain ceremonies where the monks go first before the nuns.
But we can't change the vows, because they go back to the Buddha, it's thought, and he didn't put in place any method for changing them. Except by being truly radical like the Japanese.
The Japanese monks and nuns don't use the Vinaya at all, but have this approach based on the Bodhisattva vows so don't have this issue. They can even marry indeed often do in Japan.
A similar thing is true for Ticht Nhat Hanh who is also in a Zen tradition. He has bypassed the whole thing by making up new vows that are not based on the traditional Vinaya at all.
His nuns take the fourteen vows of interbeing, and these are the same vows for men and for women. And apart from celibacy are also identical for lay practitioners and the nuns and monks.