In this fanfiction, it could be that Harry's power stems from his experiences. He has faced numerous dark wizards and challenges, which have forced him to grow stronger. Merlin, on the other hand, might not have had such intense and varied experiences. So, through his trials, Harry has developed powers that surpass Merlin's.
Well, in some fanfictions, Harry Potter might be seen as more powerful than Merlin because Harry has faced and defeated Voldemort. That's a huge accomplishment. Merlin, while very powerful in his own right, didn't have to deal with a dark wizard as complex and powerful as Voldemort. Harry's ability to survive the Killing Curse as a baby also gives him a sort of 'chosen one' status that could be seen as making him more powerful.
Magic knowledge. Harry has a lot of knowledge from Hogwarts, which could be more comprehensive than what Merlin had. So in fanfiction, this knowledge could be used to show he's more powerful.
For Harry, he might be shown with enhanced spell - casting speed and accuracy. His Patronus could be stronger or have new abilities. As for Merlin, his traditional powers may be toned down. Maybe his ability to foresee the future is not as accurate as it was originally depicted, making Harry seem more powerful in comparison.
One reason could be his pure heart. Harry's pure intentions and lack of desire for power for power's sake gives him an edge. His magic is not corrupted like Voldemort's. It flows more freely and is more in tune with the natural order of magic. So, when he casts spells, they are more effective.
Maybe in this fanfiction, Harry has a hidden power within him that is only revealed later. It could be something related to his family heritage that Dumbledore doesn't possess. Also, the author might have decided to give Harry more power to explore different storylines. For instance, Harry could be more powerful because he has a stronger bond with the magical creatures, which gives him additional powers that Dumbledore lacks.
As for Merlin, in this fanfiction, he is likely to be portrayed as less powerful than we usually think. His image might be adjusted to highlight Harry's strength. Maybe Merlin is shown as having some limitations in his magic that Harry doesn't have. However, it could also be that the fanfiction shows a different aspect of Merlin, like he might be more focused on other non - combat - related magic while Harry is stronger in direct magical combat.
It's hard to say. Peter Pan has his unique abilities like flight and his connection to Neverland's magic which gives him an edge in his own territory. However, Merlin is a very powerful wizard with a vast knowledge of magic. If they were in Camelot, Merlin might have the upper hand due to his familiarity with the local magic and his experience dealing with different magical threats there.
Harry may show greater power in his connection to the magical world around him. He has always had a special bond with Hogwarts. In the fanfiction, this bond could be enhanced. So, when Voldemort tries to attack the school, Harry is able to draw on the magic of Hogwarts itself. He can use the ancient magic stored within the castle walls to create powerful shields and offensive spells that are far more potent than anything Voldemort can muster.
Merlin might use his magic skills to help Harry. For example, he could use his knowledge of ancient spells to protect Harry from dark magic. Maybe he helps Harry in battles by creating magical shields or illusions to deceive the enemies.