Harry could be more empathetic. Since Remus has faced so much discrimination as a werewolf, Harry would grow up understanding the pain of being an outcast. This would make him more sensitive to the feelings of others, like the house - elves or other marginalized groups in the wizarding world. Also, Sirius's loyalty to his friends would make Harry value friendship even more deeply.
His magical abilities might develop differently. Sirius was a very talented wizard, and Remus was highly educated. They could train Harry in different areas of magic. He might be better at defensive magic earlier on, as Sirius was excellent at dueling. And his knowledge of ancient magic or magical creatures could be more extensive due to Remus's influence.
He'd probably be more confident. With Sirius and Remus as his guardians, he'd have two strong male figures who believe in him wholeheartedly. Sirius's boldness and Remus's wisdom would rub off on him. He might be less hesitant in taking risks and more assertive in his actions.
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.
His Hogwarts experience would be very different. Firstly, he would likely enter Hogwarts with a much higher level of magical knowledge. James and Sirius could have taught him a great deal before he started school. So, he might be ahead in classes like Transfiguration and Defense Against the Dark Arts. Secondly, his social status would be different. Everyone would know he is the son of James Potter, a popular and talented wizard. This could lead to him being more of a center of attention, and he might have a different group of friends. Instead of Ron and Hermione at first, he could befriend students from more well - known wizarding families.
He might be more traditional in his magic use as his grandparents would likely teach him older spells. Also, he could be more family - oriented since he was raised by family. He might be less impulsive as his grandparents could have instilled more patience in him.
He'd probably be more confident. Growing up with Lily, he'd have a strong female role model. He'd likely be more in touch with his emotions as Lily would encourage him to express himself. Also, his magical abilities might be more refined from an early age as Lily could start teaching him basic magic earlier than he learned in the original story.
He'd be more in tune with the sea. He might be calmer, like the ebb and flow of the ocean. His reactions to things would be more measured as he's used to the slow, powerful nature of the sea. For example, instead of getting angry quickly, he'd wait and think like the sea does before a big wave hits.
Naruto's social skills would also be different. Instead of being the lonely outcast, he would be part of a family. He would interact with other ninja kids in a more positive way. His parents could also guide him in making friends. He might be more diplomatic in his relationships because he has seen how his father, as the Hokage, dealt with people. This would all contribute to a very different Naruto compared to the one we know from the original series.
If Harry was raised by Sirius, his personality would be more rebellious. Sirius was always against the traditional ways of the wizarding world. Harry would be influenced by this and might question authority more often. Also, he would be more confident as Sirius would encourage him to be himself and use his talents. Harry would grow up with a stronger sense of self - worth, knowing that he was loved and supported by Sirius.
His magical abilities could be different in many ways. Since James was a strong wizard, and Remus was a werewolf with his own unique magical condition, Harry might have a more complex magic. He could potentially have an easier time with transfiguration, given James' skills in that area. And perhaps some connection to the more primal or lunar - influenced magic due to Remus. For example, he might have an enhanced ability to sense danger during the full moon.
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.