Eowyn of The Lord of the Rings and Jyn of Rogue One both come from similar circumstances and share many character traits and a similar character arc. Both characters live in a time of war and both are essentially orphans. Jyn is raised from a young age without her parents, and Eowyn's parents are both dead.
Who raises them instead? A father figure, Saw Gerrera in Jyn's case and her uncle King Theoden in Eowyn's case. Interestingly, both of these father figures deteriorate in some way before the eyes of their "daughters." Saw becomes increasingly paranoid and questionable in his rebellion tactics, all of which makes Jyn uncomfortable to watch or take part in. Theoden basically falls into an uncaring lethargy that makes him unable to care for his land and his people--and this would presumably hurt Eowyn especially because she is someone who wants to be able to do more to fight for her people than she is allowed to do.
This brings us to the wartime traits of both women. Saw trained Jyn because he knew that she would need to be able to take care of herself in order to survive. So Jyn in skilled both in various types of combat and in battle tactics. I don't see that Jyn likes battle, but she does like being successful and skilled at combat; especially when she is young, she gets excited to see what she is capable of. Eowyn is also skilled--but she loves war. At least, she thinks she does (before she actually takes part in it). Eowyn loves the idea that she comes from a people who are skilled in battle, and she relishes the idea that she shares that skill. She believes that this makes her mightier.
Jyn is the rebel, but in fact Eowyn is much more rebellious than Jyn. Eowyn disguises herself behind a cloak to go with the men of Rohan to aid Gondor. She doesn't ask anyone's permission (because she knows she won't get it); she just goes. But Eowyn, contrary to how she is sometimes pictured, goes with a taste for death (which I'll get to later). Basically Eowyn leaves saying, I don't care how things are supposed to be done, this is what I want to do, so I'll do it. Jyn, on the other hand, is more forced by circumstances to take part in war. Jyn hates war because she sees what it does to people and how it ruins lives. You could say she's more mature than Eowyn in that regard. However, Jyn does still have a streak of defiance to her. Simply consider her defiance of war. She doesn't want to be part of the Empire or the Rebellion after seeing all of the questionable things that Saw was doing and causing. So she tries to just escape it all and stay under the radar (which, of course, she unable to do for long). Like Eowyn, Jyn isn't the type of person to let anyone tell her what to do.
Now we come to the broken part of these two characters. They're both, at a certain point, unable to care about anything anymore. Not in the nonchalant sense of, oh, you can't hurt me with your words, all of that bounces off of me. Not like that. I mean that they literally can't bring themselves to care about anything. They're broken. You could probably say that they're both depressed, specifically by circumstances. Jyn basically feels like she has nothing left to live for. She's lost both her parents, she believes that her father has betrayed her, Saw Gerrera failed her, and she's constantly on the run. To her, the Rebellion causes more pain than it fixes. And so her own life hardly seems worth it anymore. Eowyn, as well, goes riding toward Gondor with too much of a fixation on death. She wanted to be with Aragorn because she wanted to be high and mighty, and now she sees nothing of worth left in her life, so she thinks that losing herself in battle is her only option now. Both characters are done with the mess that is life.
For two characters who are praised for being inspirational, they're in very dark places. I think people tend to gloss over this darkness in favor of bland statements about "strong women."
However. Both Jyn and Eowyn find peace, and therein lies the inspiration.
When Eowyn takes part in battle, she discovers something she didn't go seeking. That is, she begins to discover it. Truly, her journey toward peace happens in the Houses of Healing, specifically during her time spent with Faramir. In battle, Eowyn sees death in reality--and sees that it is not poetic and grand. It is sad. She's still restless at first in the Houses of Healing, but with time she's able to let go of that restless spirit, that sense of discontent, and that desire for war. She tells Faramir that she will no longer be a shield maiden; instead, she will delight in all things that grow and are alive. She trades death for life. Now, Eowyn's happy ending can make Jyn's look rather bleak. However, Jyn's is just as happy, in a certain sense of the word. Jyn has been haunted since she was a child. When she leads the Rogue One mission, she has finally found something she is willing to fight for and a team that she is willing to stand with. She is able to die knowing that she has made the right choice, a choice that will make a positive difference, and that she has found a home. Jyn has been homeless for a long time by this point, so finding a home and family means everything to her.
I also want to note that Cassian and Faramir are quite similar: they're both gentle-natured people who are born into a wartime setting and are very good at making their way in war. Because they're skilled warriors Eowyn and Jyn respect them, and because their personalities are not traditional warrior types (you can imagine them both being very content during peacetime) they're able to help bring these two haunted characters towards peace.