Short answer is: a lot. Their goals and motivations are so alike Miura even reused almost the same dialog in some spots. Casca and Farnese both struggle(d) to get closer to their idols, Griffith and Guts, respectively, but there are still a few small, but important differences.
For this reason, Farnese will strongly be able to relate Casca and help her process her memories, especially in regards to both Guts and Griffith. They will be able to compare their experiences and hopefully both conclude how much healthier any interaction with Guts is.
A Catalyst of Change
For Casca, the event that changed her deeply was her encounter with Griffith, when he raided the carriages as she was being assaulted by the noble. If you look closely at what is happening, it’s not just that Griffith “saves” her – Griffith cuts off the noble’s ear, throws his sword towards her and asks her to take up the sword if she has something to protect (her pride included). She then kills the noble who fell onto the sword.
Griffith empowered Casca to take matters into her own hands and fight. The blanket she was given is also symbolic for the warmth she was gifted with.
For Farnese, the final straw was the rebirth scene in the Conviction Arc, covered in Volume 20 and onwards, where her belief came crumbling down like the Tower of Conviction itself – a visual symbolism that’s used by Miura a couple of times (the events made her follow Guts are explained here in more detail).
Here, the moment Farnese started to change can be pinpointed to from after Mozgus was defeated. Guts, Farnese, Serpico, and a few others are struggling to fight back the evil blob of spirits on the walls of Albion. Guts redirects Farnese’s attention when she is about to pray and calls her out to use her own torch instead.
Guts empowered Farnese to act and use her own light, as symbolized by the torch.
This moment is so important she even recalls it in her dreams. We even see a Berserker Guts gnawing on Mozgus that can be taken as symbolic to their final fight as well.
Infatuation and selfless Devotion
Casca, as a result of Griffith saving her from the noble, giving her a sword to fight with and a blanket to keep herself warm, decided to join him. Being sold to a noble, her family wasn’t expecting her to return and she had no where else to go.
Casca gave her best doing her job, commanding her men and growing strong. She became a very capable fighter and leader.
After Griffith was captured for sleeping with Princess Charlotte, the Hawks were surrounded by the Midland Army. It was through her leadership skills and her selfless efforts they were kept alive for an entire year. It took quite a toll on her as well.
She not only defended the Hawks for the sake of Griffith’s dream – I believe she somewhere also found solace that the Hawks were like family to her. It may not be as far-fetched as you think, given that in episode 359, the way she speaks to her companions is very warm family-like as well.
Farnese notices that Guts has always been trying to protect Casca, even from before she joined him, that means during the events of the Tower of Conviction.
When Farnese had the possibility to return to her old life when she ran away to get a ship, her father states in volume 29 that she would face a trial for not reporting back after the events of Albion – she cannot go back without literally being placed into a prison, either.
As the journey goes on, she realizes Guts’ pure intent to protect Casca, despite of her unable to return anything for him. It is also very relatable to her. Because of this, she wishes to drive away Casca’s darkness to return the light Guts had given to her during the events of the rebirth scene.
Note how Farnese also does not receive anything in return doing so – at least not directly. Her feelings of infatuation and admiration are not returned by Guts at all, however, he lets her know that her friendship and contributions are definitely valued by him – you cannot say the same about Griffith and Casca.
Incapacity to get close
Both Farnese and Casca struggle to get close to the men they are infatuated with.
In the Golden Age, Guts possibly is affected by Casca’s lack of initiative and tries to bring her closer to Griffith because he wants to do her a favor or make life easier for her (“Must be rough being a woman”).
Now we see Roderick fulfilling a similar function in regards to Guts and Farnese. Maybe he’s not actively trying to bring them closer, but he is reassuring Farnese that her contributions are important to Guts and the party as whole, making a comparison to the crew of a ship.
Interaction: Warm vs Cold
This is where the big difference between Farnese and Casca hits.
Sometimes, we do see Griffith reassuring Casca, but as you read into the Golden Age, these instances become rarer and rarer.
During the events of the Golden Age, Casca felt that Griffith was distant and unreachable to her.
For contrast, the instances of Guts and Farnese interacting in a meaningful and nurturing way are actually accumulating as you read on.
In the most recent arcs you see her caring for Guts’ well-being and in return, Guts is praising and reassuring her whenever she needs it. Guts remains reachable to her. I am under the impression they will only grow closer as friends as the series continues.
The following panels illustrating the tone of Guts and Farnese’s most recent interactions are taken from volume 36 and 37.
How they interact seems healthy, natural and in a platonic way, mutual as well. It’s lovely to see, really.
And Griffith? Wellp. I want to show one instance where Griffith did praise Casca once, but there literally is none. Griffith never said a word of praise to anyone except for Guts, as Casca points out during the Cliff Scene.
This is also why she was so jealous of Guts in the beginning.
Another reason was that Casca’s relationship to Griffith was strictly one-sided and he didn’t regard her as special enough to be worthy of any praise. Now, why Griffith would think that? Maybe because Guts was the only one who had the skill and stubbornness to refuse to join the Hawks and not be a “sheep” flocking to his shepherd. This is most fascinating, actually.
Summary
Because Farnese’s and Casca’s experiences are so familiar they will be able to relate to the other on a very deep level. Farnese’s capacity to relate to Casca will give the latter an important support pillar for processing the trauma around the Eclipse and eventually, bring her and Guts back together. I can already see those three becoming best friends already.
Berserk Analysis 
I don’t thing stubbornness and the refuse to join the Hawks played a big role in Griffith devotion to Guts.
Let’s face it, what Griffith needed for his band was warriors and Guts was/is more than awesome, no one could compare to him. And despite Guts’s lack of goals or dreams, Griffith sees Guts as an equal o even (secretly) better than him, and objectively Guts truly is better than Griffith as a warrior.
There’s one thing I always took in mind when talking Guts and Griffith relation. In the assault of Doldrey, Griffith draw an attack plan inspired in Guts fight against Bazuso, putting the band between the river and the enemy with no posible withdrawal, it was death or glory, hoping that as Guts did, the band would fight harder. That was a sick plan and too risky for the band. Viewing where his leader had put them Corkus said Griffith has gone insane, what he will never know is that Griffith did that because of the admiration he had towards Guts. I think even Guts didn’t notice that detail, or does he?
I believe Guts didn’t notice at all the admiration Griffith had for him, maybe because Griffith valued what Guts do but not who Guts is, and that second thing is what Guts needed instead.
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