On a certain level, Harry Potter and Percy Jackson are very similar stories. Both follow a child with unruly black hair and green eyes as he discovers a hidden inherited power inside himself and joins a community meant to teach children like him how to control that power. Both feature a central villain killed long ago and reborn through ritual in the fourth book, and a blond male antagonist that begins as a slightly incompetent threat but is eventually forced to obey said villain through threat and abuse. They are, on the surface, parallel stories.
There is something fundamentally different between the two, though. Percy Jackson is a Slytherin. His antagonist, Luke Castellan, is a Gryffindor. Please don't run screaming, I'm here to explain myself.
Disclaimer: For the record, 1) We're focusing on the One True Percy Characterization in Percy Jackson and the Olympians rather than the Percy in the later books, since his personality changes wildly between them. 2) We're going with Hogwarts houses being based on what your actual personality traits are rather than with the fan theories that sorting is based on actions or what personality traits you value, since those theories mostly stems from slips in the sorting algorithm where JK Rowling didn't entirely think through where she put her characters aside from Gryffindor = Good and Slytherin = Bad. I'll explain that bold claim in a second, too.)
In most people's minds, it seems, Percy Jackson is a Hufflepuff. It makes sense, I guess. He's friendly, kindhearted, and determined. The books say outright that his fatal flaw is his loyalty. It fits, on the surface, but any deeper dive into this idea proves it faulty. Percy is not patient. He does not value fairness when it doesn't benefit him (Just look at his reaction any time someone tells him he can't go on a quest, or the way he tricks monsters through talk and rigged games of Rock Paper Scissors). His way of approaching and handling the world is often far more aggressive, impertinent, and competitive than a Hufflepuff's. While some of his major characteristics line up, so many of his personality traits simply don't. And while he shares the reckless courage of Gryffindor and cleverness of Ravenclaw, neither house embodies his dominant personality traits. All of those traits, including his loyalty, actually point toward what many consider the opposite side of the sorting hat spectrum: Slytherin.
Slytherins are ambitious, determined, and willing to do anything to achieve their goals, and Percy exhibits every one of those traits both as a leader and a friend. Rather than glory, wisdom, or fairness, Slytherins often want power, a quality that often ends up being Percy's true fatal flaw when he stumbles into new abilities, from controlling the water in the horse stables in Battle of the Labyrinth to controlling the poison in Tartarus in House of Hades, and is the source of much of his resentment toward the gods as he battles them for control over his own life. Slytherins are resourceful and cunning, and not only does Percy's entire approach to battle rely on his ability to deceive and distract foes before his physical ability, but his problem solving and general manner of thinking rely on unconventional creativity. He tricks Crusty into lying in his own bed and Ares into letting him stand in the ocean in The Lightning Thief. He manipulates Luke into revealing his plan through Iris message in Sea of Monsters. He talks his way out of every fight he can, so much so that Kronos calls him out on it in The Last Olympian. Though he's often thought of as impulsive, Percy truly relies on his ability to think through his problems. Most important to the Slytherin vs. Hufflepuff debate, though, is that Slytherins believe in fraternity, a harsh loyalty to their closest kin that mirrors Percy's sense of personal loyalty far better than the general loyalty Hufflepuffs share -- "To save a friend, you would sacrifice the world." Every personality trait, from the dominant to the undercurrents, are, through and through, Slytherin traits.
I think the main reason people are reluctant to see that, though, is that, whether they'll admit it or not, people like to equate Slytherin with being evil, despite there being nothing inherently evil about them. Obviously, in Harry Potter, they're a one dimensional, and, thus, evil house because the majority of JK Rowling's thinking when it comes to the houses is one dimensional itself. The housing system is an interesting idea, but often poorly written. The fact that people are still arguing about whether your house is determined by personality, actions, or values proves that. In Harry Potter, nearly every hero comes from Gryffindor and, while not all Slytherins are evil (though Jo never actually proves that in her writing), "there's not a single witch or wizard who went bad who wasn't in Slytherin." Slytherin personality traits apparently make them Death Eaters and blood-purists in Harry Potter, as if the Sorting Hat purposefully chooses racist ten year olds for Slytherin and only claims to base its sorting on whether they are resourceful and ambitious, but, in the real world, as a set of personality traits used to sort people for fun, they can be shared by anyone. And, whether you like it or not, Percy's personality lines up with Slytherin more than any other house.
And then there's Luke. It's easy to sort Luke into Slytherin because he's a villain. That's what JK set us up for. There's something different about Luke as an antagonist, though. He's central to just about the only popular Children's/YA plotline about a protagonist stopping the antagonist's revolution rather than starting one. The entire twist at the end of The Last Olympian was that the "hero" mentioned in the prophecy was Luke, not Percy. Just the other day, my group chat devolved from coherent conversation on PJO to everyone yelling, in all caps, "LUKE WAS RIGHT," "LUKE WAS RIGHT," "LUKE WAS RIGHT." Things clearly aren't as straight forward as they appear when it comes to this kid.
I wouldn't call Luke cunning or resourceful. Yes, he tricks Percy in TLT and Annabeth in TTC, but those are straight forward lies more than thought-out plans based in actual cunning or craft. He relies on strength and force far more than his ability to deceive. He isn't led by a want for power or, in the end, personal advancement, since he knows by TTC that he will reap none of the benefits of his revolution, but is forwarded by a want to prevent other demigods from going through the same abandonment and dejection he did. He believes the gods are corrupt and that this revolution is for the greater good. He gives his body and his life to the cause so that others can experience the glory he feels he was robbed of on his quest so many years ago. I'm sure you can tell by now, but just about every trait I just listed belongs to Gryffindor -- a team of bold leaders pushed forward by a righteous and reckless sense of heroics.
So, when a central villain killed long ago is reborn through ritual in the fourth book, a wounded Gryffindor, Harry Potter, decides it's best to die fighting, and a wounded Slytherin, Percy Jackson, decides it's better to run. When a dark-haired, green-eyed boy discovers a hidden inherited power inside himself, Harry Potter fears the extra power Voldemort's soul lends him where Percy Jackson digs deeper until that power becomes a threat to his own and everyone else's safety. When a blond male antagonist finds himself under the thumb of an ancient evil, Draco Malfoy obeys to protect his own life and Luke Castellan obeys to propel his cause.
On the surface, these narratives are similar. Where they differ is in the complexity of the idea of what makes right and wrong, or what makes Slytherin and Gryffindor. In Harry Potter, the distinctions between houses are equal to the line between good and bad, both clear, straight forward, and linear. In Percy Jackson, Rick Riordan's decision to flip those ideas on their head and create a protagonist and antagonist that are so similar in all but their priorities, thus creating a Slytherin protagonist and Gryffindor antagonist, means those lines are never clear. Percy and Luke are two sides of the same coin, parallel to the point where Percy's ideologies are shifted by Luke's, who he still appreciates as a mentor years later, but they are separate in their approaches. Harry's tie to Slytherin and his antagonist are the literal piece of Voldemort living inside him and the barest of parallels that mainly emphasizes how different the paths Harry and Voldemort took were, because these houses represent a clear sense of good and evil in Jo's mind. Percy's tie to his antagonist and to Slytherin are embedded in his personality, and that adds a level of complexity to the idea of good and evil, and Hogwarts houses, that JK Rowling's writing never had.