She would likely have a different view of family. Growing up with the Delacours, she would have a more flamboyant and loving family environment. This would make her more confident in showing affection and relying on family support. In contrast, the original Harry had a rather lonely childhood until he discovered the wizarding world. Her relationships with others would also be different. She might be more diplomatic, having learned from the Delacour family's social skills, which could lead to different interactions with characters like Snape or Dumbledore.
Well, she would be much more hardened. The original Harry grew up in a relatively normal, albeit unloving, muggle household. But a female Harry in Arkham would have seen and experienced true horror and madness from a young age. So she'd be more cynical and less trusting.
Well, for starters, her moral compass would likely be more complex. The original Harry had a strong sense of right and wrong based on the values of the wizarding world. But a female Harry raised by demons might question those values more. She might be more cynical at first. For example, she may not see things like stealing magic items as completely wrong if she was taught by demons that survival is the most important thing.
She would be far more unpredictable. The original Harry was quite noble and adhered to a set of moral values. A female Harry raised by the Joker might not have such a clear - cut sense of right and wrong. She could be more likely to play pranks and use her magic in ways that are not strictly 'good'. For example, she might use magic to create chaos in a situation just for the fun of it, rather than to solve a problem in an orderly manner like the original Harry.
He'd probably be more refined. The Delacours are a posh family, so he might have better manners.
Her character might be more confident earlier on. Since Dorea Black is from a magical family, Fem Harry would likely be exposed to magic and magical culture from a very young age. She wouldn't have the same feelings of being an outcast that the original Harry had at the Dursleys. This could lead to her being more self - assured when she arrives at Hogwarts.
He'd probably be more refined. The Delacours are known for their elegance, so Harry might have better manners and a more sophisticated way of speaking.
In the original Harry Potter story, Harry grows up in a somewhat ordinary (albeit cruel) Muggle household and then enters the wizarding world. In a 'Harry Potter raised by Catwoman' fanfiction, he'd be raised in a world full of crime - fighting (sort of) and stealth. His moral compass would be shaped by Catwoman's actions. He might not have the same friends as in the original story. For example, Hermione might not be as interested in befriending a street - smart Harry as she was in the book - smart Harry. His relationship with magic would be different too. He might use magic more as a tool for his Catwoman - inspired activities rather than for academic or traditional wizarding purposes.
Harry would likely be more wild in a sense. Dragons live by their instincts, and he'd pick up on that. His magical abilities could be more primal. Instead of relying on the spells taught in Hogwarts, he might use magic in a more raw and unrefined way. Also, his sense of loyalty might be more towards the dragons rather than the wizarding community initially.
He would be more refined. Royal upbringing would instill in him a sense of propriety and elegance that he lacks in the original story.
Well, in such fanfictions, her character development might be more influenced by her mother's traits. Since she looks like her mother, perhaps she has a more gentle and kind - hearted start compared to the original Harry. She might be more socially adept from the beginning, as her mother was popular. And she could use her resemblance to her mother to her advantage in certain situations, like getting on the good side of those who knew her mother well.