They would probably become like brothers. With Snape as their common father figure, they would have to learn to get along. Harry might be more forgiving of Draco's past actions, and Draco would have to let go of his animosity towards Harry.
The relationship would be drastically different. Harry, who has always seen Snape as a rather unlikable figure, would start to see him in a new light. He might come to respect Snape as a father figure. Draco, who has some connection to Snape through his family, would now have a more personal and perhaps more positive relationship with Snape. Snape himself would have to soften his usual harsh demeanor towards Harry. And between Harry and Draco, they would be forced to get along better as they are now under the same roof. They might start to understand each other's insecurities and backgrounds more.
In the fanfiction, their relationship would be complex at the start. Snape, having his own demons and secrets, would be a bit of an enigma to Draco. Draco, on the other hand, would be dealing with the loss of his family's status. Snape would start by providing a stable home for Draco. As they interact more, Draco would notice Snape's small acts of kindness. Snape would encourage Draco to explore his own identity outside of the Malfoy name. This would lead to a closer relationship, with Snape teaching Draco about things like loyalty, sacrifice, and the true nature of magic, and Draco in turn bringing out a more human side of Snape.
In such a fanfiction, the plot could involve Snape taking on the role of a father figure to Harry and Draco. He might use his knowledge and skills to protect them from the various threats in the wizarding world. Snape could also teach them advanced magic, which they might not learn otherwise in Hogwarts. And there would likely be a lot of emotional growth for both Harry and Draco as they deal with their new family situation and their past traumas.
It could change in a more positive way. In detention, they might have to rely on each other to get through Snape's tasks. If they are made to work on a complex magical experiment, they would need to communicate. This communication could break down some of the barriers between them. Maybe they start to exchange a few friendly words outside of detention, slowly building a more amicable relationship.
At first, it would become more strained. Harry would likely be angry and hurt by Draco's actions that made him cry, so he might avoid Draco even more than before. He might also be more on guard around Draco, not trusting him at all.
At first, it might be rocky. Draco, used to his pure - blood superiority, would be a bit resentful of having to share his home and life with Harry. But as time passes, they'd start to see each other's good qualities. Harry's bravery would impress Draco, and Draco's cunning could earn Harry's respect. Eventually, they'd become close friends, always having each other's backs.
Well, it would likely make their relationship much more complex. Instead of the typical rivalry, there could be a sense of family obligation. Draco might feel protective of 'her' in a different way than he would a male Harry. He might be torn between his family's views and this new connection to Harry.
One possible plot could be that Snape, seeing the troubled situations of both Harry and Draco, decides to take them under his wing. He could start by teaching them more advanced magic in a strict but fair way. Harry might initially be resistant as he has his own ideas about Snape, but gradually realizes Snape's good intentions. Draco, on the other hand, might struggle with the idea of being under Snape's authority as he is used to his family's influence. They could all learn to live together, with Snape guiding them through the challenges of Hogwarts and the wizarding world at large.
Well, it would change the story a great deal. Firstly, Harry would have a more stable home environment with Severus as his guardian. He wouldn't be so alone at the Dursleys'. Draco, on the other hand, might learn different values from Severus rather than just pure - blood supremacy from his family. And Hermione would have an adult figure in the wizarding world who truly understood her thirst for knowledge. The whole dynamic between the three of them would shift from rivalry to more of a sibling - like relationship under Severus' care.
If Harry were Draco's older brother in this fanfiction, their relationship at Hogwarts would be a total mess - up of the original dynamic. Harry would be constantly torn between the Gryffindor values he adheres to and his family bond with Draco. Draco might start to question his Slytherin - only ideology because of his connection to Harry. For example, they might find themselves in situations where they have to choose between their house loyalties and their new - found brotherly bond, like during the Quidditch matches or the Triwizard Tournament.