The Vampire Diaries and its spin-off, The Originals, featured epic stories with a focus on family, especially two brothers. In each respective show, one brother represented the good (Stefan and Elijah), and the other brother represented the bad (Damon and Klaus). Although of course, things weren't as easy as that. The complexity of each brother was revealed throughout the show.
Still, bad boys Damon and Klaus do parallel each other. Below are five similarities we see between the two characters and five differences.
Similar: Daddy Issues
Klaus ran for centuries from his father Mikael, a vampire who wanted nothing more than to kill Klaus after discovering that he wasn't his. With Mikael hunting him with a vengeance, he became the only person that Klaus fears.
While Damon doesn't have daddy issues as seriously as Klaus, he still has them, as hi father favored Stefan. Additionally, Damon's father constantly disapproved of him. In the end, Damon stops trying to get his father's approval. However, he keeps the insecurity that others prefer Stefan over him, like his dad once did.
Different: Control and Chaos
Klaus thrives on power and he likes to control everything from whom his sister dates to who has access to his child. Even in moments where he allows himself to be vulnerable, such as in his sessions with Camille, Klaus still controls how they and erases her memory of them afterwards.
Damon, on the other hand, thrives on chaos. He breaks the rules and doesn't really care about seeking out power. He would rather be the agent working in the shadows than out in the light broadcasting all that he has done.
Similar: Punishes Their Sibling(s)
From the first time we meet Damon, he has it out for Stefan. He kills Stefan's best friend Lexi without batting an eyelash. He doesn't care about Stefan or his feelings. Instead, Damon nurses the grudge that Stefan made him complete his vampire transformation. Later, we see that Damon really loves Stefan; however, he still hurts Stefan time and time again.
Klaus keeps special daggers ready for all of his siblings. These daggers make them "sleep," or briefly go into a death-like state. He threatens them often with this. Finn, the oldest brother, has been daggered most of his vampire life. Rebekah, whenever she falls for the wrong guy, is daggered to teach her a lesson.
Different: Age and Power
Klaus, as an original vampire and a hybrid, is much older and more powerful than Damon. Klaus sired many vampires, and he is Damon's vampire ancestor. Klaus' power is proven when Damon is bitten, and his hybrid blood saves Damon.
If it weren't for this gesture, Damon wouldn't have lasted to be the badass vampire we grow to love on The Vampire Diaries. Even at Klaus' very weakest, he is still more powerful than Damon.
Similar: Changed For Another
Both Klaus and Damon change their bad boy ways for someone else. Damon changes for Elena. He even becomes human so that he can have a full human life with her.
The person Klaus changes for is his daughter Hope. He becomes aware that he has made the world not safe for her due to the amount of enemies he created. His past hurts his present. Still, he fights to provide safety for Hope, trusting his siblings for help. Hope brought out the best part of Klaus.
Different: Family Loyalty
Klaus' motto with his family is, "always and forever." Despite his often callous treatment of his family, he does love and protect them. In The Originals, he actually allowed himself to be captured by Marcel in order to protect his family. While he may be a tyrant, he cares deeply for his siblings, especially Elijah and Rebekah.
Damon does care for Stefan, but he has little connection to the rest of his family. In Season 1, he actually kills the Salvatore descendant who has been maintaining the house. He also threatens another descendant. It is only Stefan whom Damon cares for, and that care took some time to manifest.
Similar: Is a Romantic
Damon came back to Mystic Falls in order to save Katherine, thinking that she was magically trapped underneath the church since the Civil War. When Katherine was with both brothers, Damon was the one who willingly wanted to be a vampire in order to be with her. He loved her for hundreds of years. Later, that intensity of love transferred to Elena.
From sending Caroline a dress and a portrait, Klaus demonstrates his romantic tendencies. When he comes back to Mystic Falls for her high school graduation, he tells Caroline that Tyler is her first love, but he will be her last love. While Klaus manipulates a lot, he is earnest when he says these words, showing his romantic nature.
Different: Develops Strong Friendships
Apart from Camille and Marcel (though he considered Marcel his son rather than his friend), Klaus doesn't have strong friendships. Most people are wary of Klaus, knowing that he can easily change his mind and that he will always prefer his family over any friends.
In contrast, Damon develops strong friendships throughout his time in The Vampire Diaries. Bonnie starts out hating Damon, but after being imprisoned in the hell-world, they connect and become best friends. Before Bonnie, he develops a strong friendship with Alaric. When Alaric dies (the first time), Damon is with him until the end. It is a tender moment that shows how much Damon cared for Alaric and how important that friendship was.
Similar: Villains in Search of Redemption
At one point when Damon and Klaus are talking together in The Vampire Diaries, Klaus asks Damon how Elena can forgive him after he has done so many terrible things. At first Damon responds,"Some people are just more capable of forgiveness than others." Then he tells Klaus that, "If you're going to be bad, be bad with purpose, otherwise you're just not worth forgiving." This is a great moment between the two, and perhaps shows why people are quick to rationalize Damon's behavior more so than Klaus'.
Klaus' whole arc in The Originals is about redemption. Being a father to Hope gives him a chance to change. Even his family, those who have promised to stand with him "always and forever," are separating from him. In order not to be considered the villain, Klaus has to be redeemed.
Different: Wants to be Understood
Despite Klaus being the scarier villain, he really does want to be understood. This is part of the reason that he compels Camille to serve as his therapist/history writer. He wants people to realize that he is the way that he is because of things his parents did to him. On top of his father hunting him, Klaus' mother denied him his werewolf nature, so he feels like part of him is missing.
While Damon develops strong friendships and a love with Elena, he doesn't seek to be understood. He doesn't feel a need to tell his life story to anyone. In Season 3, Elena asks him why he doesn't let people see the kindness in him. Damon responds, "I don't want to have to live up to anyone's expectations." It makes one wonder what other good things that Damon has done, but that others know nothing about.