The Vampire Diaries and The Originals both had a central character who was the more flawed brother in a brother-duo. Damon and Klaus represented the brother who was less noble, empathetic, and heroic. However, a good antihero isn't necessarily a villain, but a flawed character who viewers still root for and want to succeed. Fans may not agree with their actions, but can understand them. At times, the antihero has moments where they seem like the good guy, but these moments aren't consistent.
There are many parallels between Damon and Klaus. They both have a brother who doesn't give up on them, despite being pushed away and tormented. Yet, for all of their similarities, which one is the best antihero?
Klaus: Father Issues
In flashbacks, Klaus is seen to be a sensitive, artistic, and caring brother. He comforts a young Rebekah, and he seems to idolize his older brother, Elijah. However, his father is always harsh on him. This harshness becomes more brutal when the father finds out that Klaus isn't his biological son.
Once vampires, Mikael chases Klaus and his siblings with the end-goal to kill Klaus. No doubt the reason why Klaus started to become an antihero stems from his issues with his father. He lashes out at others and tries to control them, eerily similar to his father. It takes becoming a father in The Originals to make him work through his demons and try to be better for Hope.
Damon: Unrequited Love
In the first season, Damon does horrible things once he's back in Mystic Falls. At first, it seems that he's doing it because he wants to make his brother, Stefan, suffer. That is part of it, but the key reason he's back is to free Katherine, the vampire who created both Damon and Stefan. He thinks that she's been starving in a tomb under the church. Damon has been in love with her since he first met her, and he's missed her for 145 years.
His horrible deeds are horrible indeed, but he does them in order to free Katherine. Unknown to him, she's been free this whole time and just didn't seek him out. In a vulnerable moment, he asks her if she loves him. She tells him, no, that's she's always loved Stefan.
Klaus: Controls Siblings, But Deeply Loves Them
If Klaus wants to punish his siblings, he stakes them and puts them in coffins. Some siblings he leaves staked for days, some for years, and others for centuries. Klaus constantly threatens to stake them anytime they quarrel or he's unhappy with them. Since all of his siblings are original vampires, they don't die when he stakes them, but they stay stuck in that state.
When Stefan and the group in The Vampire Diaries try to hurt Klaus, they steal his siblings' coffins. Klaus is beyond upset. As much as he may try to control and torment his siblings, he loves them and (in his weird way) tries to protect them.
Damon: Resents Stefan For Being Made a Vampire
When Damon and Stefan were turned into vampires by Katherine, Stefan initially embraced it more than Damon. In order to finish their transition, they had to drink human blood. Stefan did this immediately, but Damon had decided that he didn't want to finish his transition. Stefan convinces him to complete the transition, literally pulling Damon to a bloody neck of a "gift."
Damon makes Stefan's life all suffering, partly due to his resentment over the forced transition. While Damon seems to love being a vampire much of the time, he also doesn't like being one.
Klaus: Deep Rage and Fear of Abandonment
Klaus has a rage that he can't keep in check. He has to have control. If he feels disrespected or lacks control, he acts out. Part of his rage comes from a fear of being abandoned. If he's feared, then people won't leave him. If he controls them, then they definitely won't leave him. He can choose if he wants them gone, often by brutal means.
This changes in later seasons when he commits mass killings, partly because he wants people to abandon him, to think he's back to his old wild self. However, Caroline calls it when she realizes that he's killing potential enemies that could harm his family. So, his rage becomes one of protection, rather than due to fear of abandonment.
Damon: Is Bad With Purpose
In The Vampire Diaries, Damon and Klaus have a unique heart-to-heart. Klaus asks why Damon is always forgiven by Elena despite all the terrible things Damon has done. In part, Klaus is asking because he likes Caroline and hopes that she can forgive him. Damon says, "If you're going to be bad, be bad with purpose, otherwise you're just not worth forgiving."
Many of the bad things that Damon did, he had a purpose behind them, a purpose that others could rationalize. One example is when he gave Elena his blood even when she didn't want to be a vampire. This saved her in the end, but he still did it without her consent or desire, just like Stefan had once done to him.
Klaus: Deep Insecurity
When Klaus comes back to New Orleans in The Originals, he wants his throne back. Marcel, who Klaus sees as a son, is now the King of New Orleans. Although he loves Marcel, he wants to usurp him and take over, and he's willing to do almost anything to do it. He must be the alpha, the top, and he suffers from a deep insecurity about his power and control.
If people believe him to be weak, then they will go after him and his family. A master of self-preservation, he also preserves those he cares about. This is seen later when he sacrifices himself for his family, allowing Marcel to have him imprisoned and tortured through dark magic to help the rest. He becomes the living tether for Freya to link all of his siblings' lives to him in order to give Hayley time to figure out how to cure them, and then to free him.
Damon: Selfish and Self-Centered
If Damon were to have a huge flaw, it would be this: he is selfish and incredibly self-centered. In the first season, he's bored, so he makes Vicki a vampire. He doesn't think of her human life nor does he train her to be a vampire. Damon doesn't think of how many people are going to be hurt over her death or who she's going to hurt when she's a vampire. All he thinks of is that he's bored and needs someone to distract him.
Unfortunately, this is a flaw that it takes seasons for Damon to work through. Even in the last season, he still has this flaw, even if it's somewhat diluted.
Klaus: Redemption Narrative
Klaus's whole arc in The Originals is one of redemption. He's committed horrible atrocities in the past--some for pleasure, some for pride, and some for protection. The birth of his daughter, Hope, offers him the chance for redemption. He doesn't want Hope to fall into the same narrative, especially since she also has some of his flaws.
This isn't to say that it's easy. He makes many mistakes, but through it all, he's trying to be better, making him an antihero that fans can understand.
Damon: Becomes a Better Friend
Damon has always been selfish and self-serving. Elena had been one of the few who could get through to him. However, throughout his narrative arc, he starts to develop better friendships with Alaric and Bonnie, friends he truly cares about and who can call him out.
Enzo, an old friend who he betrayed, comes back into his life. This gives him the chance to make up for his past with him. The truth is Damon has empathy for others, but he's hidden it. Each season, he comes closer to who he was before he was a vampire. In the last episode, Damon is the good man he used to be. It just took him 8 seasons to get there.