In my opinion, it's really hard to say who would win. Jason has his Roman powers which are quite formidable, like his ability to control the winds. Percy, on the other hand, has his water - based powers which are extremely powerful especially in the right environment. In a fanfiction, it could really go either way depending on how the author wants to write it. Maybe they could end up not really fighting but joining forces against a common enemy.
A great plot twist could be that they are both being manipulated by a third force. They think they are fighting each other for their own reasons but in reality, they are being used. Maybe a god or a powerful demigod is pulling the strings. This would lead to a moment of realization and then they would have to figure out how to work together to stop the real threat. Also, a plot twist where the Mark of Athena has a different meaning for each of them could be really engaging. It could be that Percy thinks it means one thing and Jason thinks it means another and their interpretations lead to a big misunderstanding before they figure it out.
However, Jason has his own set of powerful abilities. His control over lightning gives him a great offensive power, and his ability to fly can give him an advantage in both battle and mobility. In some fanfictions where the setting is more favorable to his powers, he could be considered the most powerful. For example, in a high - altitude battle or in a place where there are a lot of electrical sources he can draw power from.
Well, Percy has been through a lot in his own story. Reading fanfiction could be a form of escapism for him. He might find it exciting to see what kind of wild ideas fans have come up with. In the fanfiction, he could discover new interpretations of the prophecy he is involved in. Also, he might be interested in seeing how fans have written about his powers and how they can be used in different situations that are not in the original book.
One common theme is loyalty. Their loyalty to each other is often explored in depth, like how they will do anything to protect one another during their adventures related to the Mark of Athena.
One interesting plot could be a competition between them for a powerful magical artifact. Percy uses his water - based powers, Jason his lightning and flight, and Nico his control over the dead to outwit each other in a race to find it.
Percy would win. He has a very strong connection to his powers. His control over water is so precise that he can use it in many creative ways during a fight. He can even use water vapor in the air to his advantage. Jason's powers, while strong, are more straightforward compared to Percy's adaptable water powers. Also, Percy has faced more life - threatening situations and has learned to be a better fighter overall in his adventures.
One interesting plot twist could be that Annabeth discovers a hidden power within herself that has nothing to do with Athena. Maybe she can suddenly communicate with mythical creatures in a way no one else can. Another could be Percy finding out that he has a long - lost sibling who is actually on the side of the enemy, but then later switches sides. And a third one might be that the Mark of Athena is actually a fake, created by an enemy to mislead the demigods and lead them into a trap.
One popular original character is a new demigod named Lyra. She has the power to control the elements of air and is often depicted as a fierce fighter. Another is a centaur named Orion who is a bit of a rebel. He doesn't follow the traditional centaur ways and often helps the demigods in unexpected ways. And then there's a nymph called Iris who has the ability to create illusions and is a bit of a trickster, which makes her really interesting in the fanfiction world.
One idea could be a new quest where Percy and Annabeth have to find a lost artifact related to Athena that was stolen by a rogue demigod. This would involve them traveling to new and dangerous places, facing off against mythical creatures they haven't encountered before.