Harry could become more secretive and distrustful. Growing up with Bellatrix, who is part of the Death Eaters and has a lot of secrets, Harry would learn to keep things to himself. He may not trust others easily, even those who seem friendly, as he has been brought up in an environment full of lies and hidden agendas.
Harry would likely be more conflicted. With Bellatrix's influence, he might have a darker edge to his personality. He could be more aggressive in his approach to problems. Sirius, on the other hand, would try to keep him on the right path, so there would be an internal struggle. He might not be as quick to trust as the original Harry, but more cautious and calculating.
Harry might be more secretive. He'd have to hide any doubts or conflicting feelings he has about the dark path he's being led down. Bellatrix would not tolerate any signs of weakness or deviation from her plans. So, he'd become very good at hiding his true self, which would make his personality complex and full of contradictions.
He would probably be more conflicted. On one hand, he would have the potential for great good, like the original Harry. But on the other hand, he would have the shadow of Bellatrix's dark deeds hanging over him. This internal conflict could make him more withdrawn at times. He might also have a fascination with the dark arts, not in an evil way, but more out of a need to understand his mother's world. This would set him apart from the Harry we know, who was always more firmly on the side of light magic.
Since McGonagall has a strong sense of justice, Harry would probably have an even more acute sense of right and wrong. He would grow up with her values of fairness and loyalty deeply ingrained. This could lead to him being more proactive in standing up for others who are being wronged, not just because of his own experiences, but because of the values he was taught by McGonagall.
He might be more feral. Growing up with a monster, he could lack some of the social graces that a normal upbringing in the wizarding world would provide. He may be more direct and less concerned with propriety.
He might be more laid - back. Canadian culture is often seen as more relaxed, so Harry could have a calmer demeanor. He wouldn't be as quick to get into arguments or be as impulsive as he sometimes was in the original story.
He might be more refined. The Delacour family seems to have a certain elegance about them. Harry could be more sophisticated in his speech and mannerisms. He may also be more confident in social situations as he would have grown up in a family used to high - society magical events.
Harry would probably be more rebellious. Remus and Sirius are not exactly the rule - following types. They've both had run - ins with the law in the wizarding world. So Harry would grow up seeing that sometimes breaking the rules is necessary for doing what's right. He might be less hesitant to take matters into his own hands.
His personality could be more open - minded. Since he's exposed to an alien culture from a young age, he might not have the same prejudices as other ninjas. He'd be more curious about different beings and ideas.
His character could become very conflicted. On one hand, he is being taught by villains, so he might be cynical and distrustful. But on the other hand, he might have an innate goodness that fights against what he's being taught. He could develop a unique set of skills, like the ability to deceive and manipulate from the villains, but also a sense of honor that comes from within.