He might have a more conflicted personality. On the inside, he has the genetic makeup of a hero as a Turtle, but the upbringing by Shredder would make him act in ways that go against his true nature. He could be constantly torn between his loyalty to Shredder and his inborn sense of right and wrong. This internal struggle could make him seem moody and unpredictable at times.
His personality would likely be more ruthless. Since Shredder is all about power and control, Leo would be taught to show no mercy. He might be more calculating in his actions compared to the Leo raised by Splinter. For example, when facing an enemy, he wouldn't hesitate to use any means necessary to win.
A possible storyline is that Leo, while being raised by Shredder, forms an unlikely friendship with one of Shredder's minions who has a bit of a conscience. This minion secretly shows Leo the other side of Shredder's actions, the harm he causes to the innocent. Through this friendship, Leo starts to see the flaws in Shredder's teachings. At the same time, he might use the skills he learned from Shredder in unexpected ways to protect those who are in danger from Shredder's schemes.
His communication style could be different too. He might be more direct and simple in his speech, like how animals communicate basic needs and emotions. He wouldn't be as interested in the complex social hierarchies and politics among demigods. Instead, he'd focus on the more straightforward relationships based on mutual respect and survival, much like the relationships in the animal kingdom.
He'd probably be more sophisticated. The Delacour family is known for their elegance and grace. Harry might have a more refined way of speaking and acting compared to his canon self. For instance, he would be more likely to use formal French wizarding greetings.
His personality would likely be more reserved and calculating. Growing up with the Malfoys, he'd be taught to keep his emotions in check and think before acting. He might be more aloof towards others outside of the pure - blood circle at first.
He'd probably become more nurturing. Leo is already a leader, but having a baby would bring out his softer side. He'd be more patient and understanding, not just with the baby but also with his brothers. For example, if his brothers made a mistake while helping with the baby, he'd be more forgiving instead of being overly critical like he might have been before.
Percy's personality would be more in tune with nature. Since Artemis has a strong connection to nature, Percy would grow up respecting and understanding it more deeply. He would probably be more solitary as well, as the hunters often keep to themselves. He might not be as quick to trust others as he used to be, having been brought up in a more exclusive group. Also, he would have a greater sense of loyalty towards Artemis and the hunt, which could make him seem a bit cold to outsiders.
His sense of humor would likely be different. Sirius has a bit of a mischievous streak, and Harry would pick up on that. He might be more prone to making jokes and playing pranks in a more light - hearted way compared to the somewhat more reserved Harry we know from the original story. Also, Harry would be more trusting of others in general, especially those in the wizarding world, as Sirius would introduce him to a more positive side of it from the start.
Percy could be more in tune with his emotions. Dionysus is associated with passion and ecstasy, so Percy might be more openly emotional, not suppressing his feelings as much as he did in the original stories. He could also be more creative, as Dionysus has an element of creativity in his domain. For example, he might be better at coming up with unique solutions to problems using his more artistic side.
He'd probably be more brooding. Growing up with Hades, he'd be exposed to the darker side of the mythological world constantly. So, instead of the somewhat upbeat Percy we know, he might be more withdrawn and moody.
He might be more feral. Growing up with a monster, he could lack some of the social graces that a normal upbringing in the wizarding world would provide. He may be more direct and less concerned with propriety.