The story would be very different. Harry would have a new set of values instilled in him by the royal family. This could affect his decisions regarding the wizarding world. For example, he might be more hesitant to engage in dangerous battles as he now has a royal position to uphold.
His living conditions would change drastically. Instead of living with the Dursleys, he'd be in a palace. He'd have servants and a much more luxurious life.
If Harry was adopted by the Queen, his social circle would expand to include important Muggle figures. This could lead to a new form of alliance between the wizarding and Muggle worlds. Also, his upbringing in the royal environment might give him more confidence and a different leadership style when it comes to fighting against Voldemort. He could use his royal connections to gain more support for the wizarding world from the Muggle side.
His living conditions would change drastically. Instead of living in the wizarding world, he'd be in palaces. He'd have servants and all the luxuries that come with royalty. His friends at Hogwarts would be replaced by new acquaintances in the royal circle. He'd have to adapt to a very different set of rules and expectations.
His magical abilities would be used in a different context. Instead of using magic mainly for school competitions or fighting Voldemort's Death Eaters, he'd be using it to combat vampires, ghouls, and other supernatural beings that Hellsing faces. His view of good and evil might also change. In the wizarding world, there were clear lines between good wizards and bad wizards. But in Hellsing, the lines between what is acceptable in the fight against evil can be blurred.
His life would change drastically. He'd be in a world with different rules. No more wands perhaps, but instead ninja tools. His friends would be ninjas. He'd have to learn to move silently and quickly like a ninja.
His life would change drastically. He'd no longer be bullied by the Dursleys. Instead, he'd grow up in a more wild and free environment. He might be more in tune with his instincts.
His life would change drastically. He'd be part of the royal family. He might have to attend many formal events instead of Quidditch matches. His friends from Hogwarts might not be able to visit him as easily. And he'd have to deal with the politics and gossip within the royal court.
His story would be radically different. He'd be part of a vampire hierarchy instead of the wizarding world's social structure. His goals might shift from defeating Voldemort to dealing with vampire - related issues, like vampire - human relations or power struggles within the vampire clans.
His story would change drastically. For one, his view of family would be different. Ashoka could provide a more loving and nurturing family environment compared to the Dursleys. His magical education might also be influenced. Maybe he would learn to combine magic with Ashoka's combat skills. His character development would be shaped by Ashoka's teachings on morality and leadership.
If Harry Potter is adopted by the Autobots in fanfiction, the story would take on a whole new dimension. Harry would be exposed to a completely different way of life and technology. His understanding of the world would expand beyond the magical realm. He might use the Autobots' technology to improve his magical devices. And the Autobots could use Harry's knowledge of magic to their advantage in their own battles. This would also introduce a new element of mystery and excitement to the story as the two different worlds collide.
He would probably be more in tune with nature. The Inuzuka's lifestyle would make him more aware of the natural world around him. He might be less bookish than in the original and more hands - on with physical activities like running and training with the clan.
His view of heroism would change. Hellboy is a very different kind of hero compared to the wizards in Harry's world. He's more of a brawler and has a darker, more gritty approach to fighting evil.