The short answer is yes and no, but to be clear, in the sense that they are both human, potentially among the best creatures of Allah even of a higher position than the angels, yes they are equal:
For Muslim men and women,- for believing men and women, for devout men
and women, for true men and women, for men and women who are patient
and constant, for men and women who humble themselves, for men and
women who give in Charity, for men and women who fast (and deny
themselves), for men and women who guard their chastity, and for men
and women who engage much in Allah's praise,- for them has Allah
prepared forgiveness and great reward. (Al-Ahzab,35)
However, it is also from Quran that Allah created every species and gave each everything that was required for it to live and experience a journey toward Allah (for human specifically: "To Allah We belong, and to Him is our return", Al-Baghareh: 156; and for other alive species: "There is not any alive being on the earth, nor a being that flies on its wings, but forms part of communities like you. Nothing have we omitted from the Book, and they all shall be gathered to their Lord in the end", Al-Ana'am:38):
قَالَ رَبُّنَا الَّذِي أَعْطَىٰ كُلَّ شَيْءٍ خَلْقَهُ ثُمَّ هَدَىٰ
He said: "Our Lord is He Who gave to each (created) thing its
[particular] form and nature [through which it is distinguished from
another thing], then gave (it) guidance." (Taahaa:50)
إِنَّا كُلَّ شَيْءٍ خَلَقْنَاهُ بِقَدَرٍ
Verily, all things have We
created in proportion and measure. (Al-Ghamar:49)
So that everything that is helped and guided differently it's because it has been created differently, with different natures, although sometimes the differences is as much small as one can easily categorize them in groups, like: human, different plant groups, different animal groups like dogs and cats, viruses etc. They all have different shapes and behavior as God has created them differently so also guided them differently, each to the extent required for itself.
Now see that males and females have different bodies and even some genes and organs are different between them, then who on the earth can claim that God should have been guided them similarly as has guided males? Not even for human alone but also for plants and animals, there is always a different between males and females in the way to live, not that because males are better or females, they are just different, although in that they are all human being, or animal or plant, are similar and equal.
In humans specifically, women are created in a way and men are created in another way, their bodies which their soul should use here in this world in the journey toward Allah is just different, so should be their souls. To put is differently, if the souls of male and female were to be equal, their bodies required for their creation were also required to be equal (see again the Ayah's referred above), and if it is not so their souls are also different. You of course know by yourself that even psychologically men and women are different. Let me even say something more, even every male is different from another when their faces, the shape of their noses, the color of their hairs and eyes, their height, and etc. are all different, however, it is told to us by the creator that the difference between men and women is much greater than the differences between women themselves or men themselves, so the rules expressed by Allah for men is different from those for women. But each person who acts in the way he/she is guided by Allah (required by its nature) would reach a place for human being, be it man or woman, a fat one or a tall one.
The last point, if you are still in doubt, see every human is everyday subjected to different tests, if everyone was equal to the others then it was a must for their tests also to be equal, and then we had not have such a world with this much varieties.
The tests for the prophets have always been more difficult than the tests for us and other common people, as their souls was different and you can see there was always a sign of prophecy in their bodies as well, like in their face or the right shoulder or etc.
However, the most important thing about human being and Elves, among all the alive beings, is that they can choose to improve and that's the reason behind all the tests of Allah, going by the rules of Allah can improve one's soul and you can see this through his/her face and/or eyes (although most of the times it is hidden to our eyes as Allah is Al-Sattar, but it is stated that after death or in the judging day the hijab's would go away). The prophets all did obey Allah in every instant of their lives so should their tests be more difficult if you care.