His Hogwarts experience would likely be very different. For one, he might be more physically fit and confident in combat situations. He could be less intimidated by the likes of Snape or Malfoy, as the Dragon Slayer would have taught him to stand up for himself. Also, he might introduce some new skills to Defense Against the Dark Arts, like dragon - slaying techniques adapted for magical creatures.
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.
His Hogwarts experience would be very different. For one, he would have a closer relationship with the hospital wing. He might not get into as many dangerous scrapes as in the original story because he would be more aware of the consequences due to Pomfrey's influence. Also, his reputation could be that of a healer - in - training rather than the 'Boy Who Lived'. His classes might be more centered around potions and herbology as he would have a natural inclination towards those subjects.
At Hogwarts, Harry might be seen as a bit of an oddity. His mother being Amelia Bones could mean that he has a reputation to uphold from the start. He could be expected to excel in certain subjects like Defense Against the Dark Arts and History of Magic more than in the original story. His family connections might also lead to some students either trying to befriend him for status or being jealous of him.
His sorting might be different. Maybe the Sorting Hat would consider his Prewett heritage more strongly and he could end up in a different house. He might also have different friends. Instead of Ron and Hermione being his closest allies from the start, he could befriend students from families who were closer to the Prewetts. His classes could be affected too. He might have a natural talent for certain subjects that were more associated with the Prewett family's magical skills.
His Hogwarts experience would likely be very different. He might be more popular right from the start, given the fame of both James and Sirius. The teachers might also have different expectations of him. For example, McGonagall might be more lenient as she had a soft spot for James. And he could have a natural talent for Quidditch, inheriting James' skills. He might also be more involved in secretive activities, like Sirius was, and get into more trouble with Filch.
His sorting could be different. Since he's a Black, the Sorting Hat might consider putting him in Slytherin more seriously. His relationships with Slytherin students would be more complex. He might not be as ostracized by them as he was in the original story. Also, his classes could be affected. Teachers who had a bias against the Blacks might treat him differently, while those who were friends with the family could give him special attention.
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.
His relationships would likely be very different. For one, he might be more of an outsider. The other students grew up in the wizarding world in a more common way, while Harry was raised by the Flamels. He could be seen as having an unfair advantage in terms of magic knowledge. But on the other hand, he might also be respected more for his unique upbringing.
Harry's magic could be stronger. Dorea's influence and knowledge of magic could have allowed Harry to tap into his magic potential more easily. Maybe he would be able to perform advanced spells earlier. Also, his magic might have a different 'flavor' so to speak. Since Dorea comes from a different magical background than the Dursleys, Harry's magic could be more attuned to the traditional wizarding ways of magic use.