He'd be tougher. Logan's no - nonsense attitude would rub off on Harry. He'd be less likely to back down from a fight.
Harry would be more of a loner. Logan isn't really one for big social groups, and growing up with him would make Harry more self - reliant and less eager to seek the company of others. Also, he'd be more attuned to his instincts. Logan lives by his gut, and Harry would learn to do the same. This could make him a more unpredictable wizard, as he'd act on his instincts rather than just following the rules of magic all the time.
If raised by Logan, Harry would have a much darker and more brooding personality. Logan has seen a lot of pain and suffering, and that would be passed on to Harry. He'd be less naive about the world, and his view of good and evil would be more nuanced. He might not blindly trust Dumbledore or the Ministry of Magic like he did in the original story. Instead, he'd be constantly questioning authority and relying on his own judgment, which he learned from Logan.
Harry would probably be more physically fit and combat - ready. Sasuke would train him in ninja ways, so he'd be better at hand - to - hand combat compared to the regular Harry. His approach to facing enemies would be more direct and less about relying solely on magic. He might also be more independent, as Sasuke is not one to encourage over - dependence on others.
He'd be tougher. Hela's not one to coddle, so Harry would have to grow up fast.
Harry would be less socialized in the typical human way. He might not understand things like friendship the same way. He could be more territorial and protective. His magic might also be affected. He might use it more instinctively, like using a spell to protect his 'territory' which in this case could be the area where his wolf pack lives.
He'd likely be much more morally ambiguous. Harry would probably have less regard for the rules and traditions of the wizarding world.
He'd be more confident. Ophis's influence would make him less likely to doubt himself.
He'd be more brooding. Growing up with Dracula, he'd be exposed to a lot of dark and serious stuff, so he'd lose some of that innocent charm he has in the original series.
Harry would probably be more reserved. Rosalie has a certain elegance and poise, and Harry might pick up on that. He may not be as quick to trust others as he was in the original story. Also, his view on magic could be different. Instead of seeing it just as a tool for good or for fun, he might see it as a way to protect himself and those he loves, similar to how Rosalie views her own vampiric abilities.
If he was raised in Italy, Harry might be more flamboyant and expressive. The Italian culture is known for its passion and strong emotions. His magical style could also be more theatrical, as he would be influenced by the Italian wizards' way of doing magic. He might be more confident in social situations, as Italians are often very sociable.
He'd be more adaptable. Quarians live in a different way than wizards, so Harry would learn to be flexible in new situations.
He would likely be more confident in his physical abilities. Yoruichi is a very capable fighter, and if she raised Harry, he would be trained in combat. So he might not be as hesitant in dangerous situations as the original Harry. He could be more likely to take risks and trust in his own strength.