Alan Moore and Brian Bolland's The Killing Joke is most infamous for The Joker's heinous attack against Barbara Gordon. After putting a bullet through her sternum, the Joker strips Barbara nude and takes photographs of her, pictures he will use to try to drive her father insane. Even in her most painful and humiliating moment, Barbara is merely a pawn in The Joker's grand plan. On top of being disabled, Barbara Gordon's agency is taken away from her. However, she takes steps up to reclaim that agency as well as heal from her trauma upon taking up the mantle of Oracle. She takes the necessary steps to heal and move on from what happened to her, not letting her trauma define her, and years later comes out of the better end of it all. Unfortunately, Jason Todd wouldn't be so lucky as this wouldn't be the last time that The Joker would commit such an egregious crime against someone close to Batman.
In Three Jokers #2 by Geoff Johns and Jason Fabok, the Joker and his two doppelgangers brutally beat Red Hood and strip him nude, similar to what was done years prior with Barbara Gordon, including the same horrific implications of Jason being stripped nude. They do this in an effort to drive Batman's sidekick insane at The Dark Knight's expense, once again using Batman's sidekick as a pawn in a bigger plan. As Batman and Batgirl try to console him, Jason immediately lashes out at his allies, refusing any help they could so much as hope to offer him in the wake of trauma.
It's understandable that Jason lashes out. After feeling abandoned in death, rejection is practically ingrained in his psyche by now. He never got the opportunity to get the same sort of help that Barbara received in the wake of her trauma. She brings this up herself later in the same issue, simultaneously explaining how her support system was vital to her healing. "Healing ... with the help of my dad. My physical therapist. And so many other people who were there for me," Batgirl explains to Red Hood. "I try to look at the positive. A tragedy that I was able to literally walk away from thanks to the people that love me." Accepting help from Batman and co. during her healing process is what helps her heal in the first place. Whereas Jason continues to refuse such help. In the same issue, Batman offers a helping hand that even he admits he should've offered years prior. "No, I don't need help. I'm good," is Jason's immediate response.
Both Barbara and Jason went through career-altering metamorphoses in the wake of their initial tragedies. While Barbara embraced a new role as Oracle, Jason adopts The Joker's old moniker, Red Hood, arguably becoming just as violent as The Clown Prince in the process. Jason allows himself to be defined by his trauma by adopting the name of his attacker. The complete opposite of Barbara, Jason refuses to distance himself from what happened to him. As a result, Jason continues to struggle to reclaim his agency in the same manner that Barbara has. One of these characters, Batgirl, took steps to recover from The Joker's trauma inflicted on her, while the other only lets that trauma fuel him, which makes it seem as if Jason is forever destined to be the same angry, bitter Red Hood.