My comparisons are purely broken down bare as you say. The Sisters of Light vs Aes Sedai for instance. The one ages slowly due to an effect on the building where they live, the other ages slowly due to the connection with magic. The one only has access to one half of the power they are capable of tapping into(additive and subtractive), the other has full access to the power they are tapping into(Saidar). In one, Men and Women are both capable of accessing both sides of the same power, the other, Men and Women each access different sides of the same power. You break it down and the details are different, how they are used are different, but in the basic bare bones of the story, they occupy the same place. One could argue that the Confessors occupy the same political position as the White Tower so therefore the Confessors are more like Aes Sedai. Write the basics of the story and they are similar, write details and they diverge.
Is there a group of female magic users? Yes. Who are they? Sisters of Light vs Aes Sedai. Details? Too many to list.
Is there a prophetical sword? Yes. What is it called? Sword of Truth vs Callendor. Details? Too many to list.
Was there an age of enlightenment? Yes. How long ago? 3000 years. How did it end? Cataclysmic war event. Details? Too many to list.
Is there a group of male magic users? No. How long since last normal group of male magic users? 300o years. Details on why they are no longer? Too many to list.
Is there a group that hunts down magic users? Yes. What are they called. Blood of the Fold vs Children of Light. Details? Too many to list.
Its the details that are different between the two stories, but the basics are relatively the same. The further along in the story you get, the less alike the stories are. That's why I said:
It looks like the two of them started off with the same world and took the story in two different directions.