If you want get a comprehensive list of ways these things are not about Egwene, that's why I wrote "Egwene's Evil". Just look for the appropriate smiley codes in each entry to find instances of her kinds of transgressions.

For some points to consider quickly,

a) A well-defined moral compass, and a passionate pursuit of justice.
Hermione Granger handed over a woman to be gang-raped by centaurs. Either she utterly fails at all the below things, or she knew damn well that centaurs' major purpose in mythology is rape. Even the Disney Hercules cartoon aluded to it portraying Hercules' encounter with Megara. Hermione HAD to know, and it is the only explanation for Umbridge later turning up in a clearly traumatized state, with no visible injuries and an extreme reaction to the simulated sound of hooves.

So Egwene is not at all unlike Hermione.

On her own, Egwene shows no interest in justice, unless by justice, you count her multiple-book-long pursuit of a woman who holds a position of power Egwene desires for herself, on the grounds of technical violations of an organization's bylaws. Not exactly morality or justice, and the narrative goes to lengths to show how close Elaida is to the same opinions as Siuan & Egwene on most Tower issues.

Egwene blackmails people in following her, ignores wrongdoing by which she can profit and allows the lie about Elaida & the Reds to stand, because she stands to gain by it, even though she knows it to be untrue, and explicitly states as much, when arguing in favor of discontinuing the practice of making all sisters swear an Oath to tell the truth. She dismisses monumental accomplishments on the part of her friends, because they might create political difficulties for herself. On issues where there is a dispute between Aes Sedai or anyone else, Egwene is only ever on the side of her group's privilege and status, and while she might tacitly acknowledge the validity of others' positions, only supports her own side. She even speaks of making Rand "see reason" when he issues a series of morally unquestionable directives, which she fears might be unpopular, and in her own stream of consciousness, doubts that Rand can be made to see reason, because she acknowledges that he is in the right. But she still favors the pragmatic, politic and popular over the just.

You can debate what these things say about her character, or the acceptability in context, but you CANNOT claim the character in question is defined by a "passionate pursuit of justice".

This is a massive case of falling for an unreliable narrator, if you apply this to Egwene. She characterizes herself thusly, but her actions give the complete lie. She is interest only in power. When knowledge is not immediately applicable to the pursuit or gain of power, she actively rejects it. She rejects Elyas, and wants nothing to do with him from the moment he tells her he cannot teach her to speak to wolves, and completely ignores the point that he CAN teach Perrin. Zero sympathy for Perrin's potential learning. She has no patience at all for Nynaeve comparing notes with Mother Guenna, framing her objection in terms of position and power. Nynaeve has moved beyond the authority of a village Wisdom, so why would she be interested in learning knowledge that can only bring power if you are aspiring to that post? Just to reiterate the point, she repeats her behavior in the very next book, on Chaendar, when Moiraine is making inquiries about Rand and the Aiel and the significance of their names and terminology. Egwene is not only uninterested in, she actively tries to forestall, this pursuit of knowledge, because it might impact her ability to gain power from the Wise Ones.
Egwene rebels against her immediate mentors and teachers, and turns against them as soon as she moves onto another. Book 3 is one long rebellion against Nynaeve; in Book 4, and through Books 5 & 6, she is flagrantly disobeying the Wise Ones, even after they catch and punish her. In the Tower, she went around the rules at every opportunity, and spent every moment from getting a lecture on living up to the Three Oaths, until Rand asked her to contribute to the fight against the Shaido, railing against the injunction to use other means to defend herself, saying she planned to use the Power as a weapon, now that there is no Amyrlin looking over her shoulder.
Egwene is the least capable of her trio of female peers, and her male counterparts of a similar age & alleged maturity level. Her area of expertise is in Tel'Aran'Rhiod, which SHOULD be the best chance for her to live up this point, as it is one of the few areas in which she could be said to have actively pursued knowledge. And Nynaeve blows her out of the water in achievements and accomplishments. Nynaeve uses T'A'R to break Moghedian's compulsion and later captures the Forsaken there, on her own ground. She will then use Moghedian to provide critical aid to Rand in fighting Rahvin, and her teaching the Salidar leadership sets up Egwene's own ascension, and provides her with the leverage to both Heal severing and force Siuan to serve Egwene instead of manipulating her.

Moiraine is not, ever, a mentor or teacher for Moiraine. Nynaeve rejects her as such for moral reasons, and sees her as an enemy for her mistreatment of her friends.

And it is Nynaeve who advocates consistently for justice, and places morality above pragmatism. It is Nynaeve who lectures the girls on justice and sentences Renna & Seta instead of killing them, which will later enable Mat to rescue Aes Sedai from captivity. Nynaeve is the hyper-scrupulous one who is so shamed by a bit of typical Aes Sedai verbal evasion that she lets Egwene have the moral high ground to terrorize her...to cover up Egwene's own deceits and explicit disobedience. It was Nynaeve who, knowing she could not forgo T'A'R as a resource who refused to lie to the Wise Ones about staying out without their instruction and permission, even as Egwene, who had already told the same lie, mocked her for it.

You cannot remotely compare Nynaeve and Egwene on the issues of morality and justice objectively. You might defend Egwene on the basis of political realities, and the difference in their vocations and interests, but then you have to live with that position as well. Nynaeve IS committed to justice and adheres strictly to her moral compass, for good or ill, while Egwene is not the former, and does not ever show any sign of the latter. Having a moral compass means not only doing the right thing, but having a clear idea of what constitutes right and wrong, a consistent principle or set of principles that guide one through situations for which there is no specific rules. Egwene operates on what is most fitting for the circumstances in which she finds herself and what she calls right and wrong are more like emotional reactions. For instance, what she overhears of Moiraine's lectures to Rand on Daes Daemar causes her to judge it as distasteful at best, but when she finds herself in a situation where it might be helpful, tries to remember it for her own use without a qualm. She almost never comes down on a course of action regarding morality, and when she does it is very uninformed (such as her variant moral standards for Rand and for Aes Sedai) and often hypocritical, such as her rebuke of the suggestion that the Warder bond be used to control male channelers, since it is simply an application of an acceptable practice. She denounces it as akin to Compulsion, when she herself coerces people into oaths that the Oath Rod effectively Compels them to keep.

The entire notion is fatuous and arbitrary. What does it matter if Egwene or Nynaeve fits the categorization of a "Hermione"? After all that category doesn't even fit the eponymous character.

Aside from the above-mentioned instance of moral turpitude, Hermione is a typically passionate adolescent, caught up in causes and pursuing justice not out of any real understanding of the concept, but from a juvenile blinkered black-and-white mentality. This is most consistently shown in her activism on behalf of house elves, which is portrayed as based on her own ignorance of the reality of their nature, and the superficial application of a principle to a species to which it does not apply. House-elves are controlled by rules of magic, they are not people with free will. Slavery is not a thing for them, any more than humans can be liberated from the enslaving dependency on oxygen.

And that's just what I came up with, off the top of my head, from reading the Harry Potter books only once.