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.
Farnese's character was shook and burnt down a couple of times before she eventually ended up joining Guts on his travels. She mostly invoked the change on her own during rebirth scene, but through Guts' subtle guidance after she joined him she found purpose and meaning. How this happened you can read in this article!
The short answer is, the Beast of Darkness is like a link to the Idea of Evil (assuming it's still canon), laying inside of Guts' subconsciousness. It is both part of him and part of the Idea of Evil. That also means Guts giving into it or not is still in his might and also … Continue reading What is the Beast of Darkness?
With Berserk being on hiatus once again, fans are violently discussing possible outcomes of events to come. Here are my predictions of the direction the next couple of Berserk chapters are perhaps going to take – especially in regards to Guts, Casca and his companions.