The Twelfth Doctor might seem more dominant at first because of his no - nonsense attitude. However, the Thirteenth Doctor's charm and adaptability could quickly make her a force to be reckoned with. In different situations, either could take the lead. For instance, if it's a scientific problem, the Twelfth Doctor's in - depth knowledge might make him dominant. But if it's about making friends with an alien species, the Thirteenth Doctor's social skills could put her in the dominant position.
I think it depends on the writer's intention. If the writer wants to show the passing of the torch, so to speak, they might make the Thirteenth Doctor more dominant. She represents the new era of the Doctor. On the other hand, if the focus is on the wisdom of experience, the Twelfth Doctor could be the more dominant one. Also, the nature of the conflict or situation in the fanfiction would play a big role in determining which Doctor seems more dominant.
In such a fanfiction, they might have an adventure together. Maybe they team up to fight a common enemy that neither could defeat alone. For example, a new, powerful alien threat that has emerged in the Doctor Who universe.
It could be the 10th Doctor. He has so much experience and knowledge about the universe, time, and different species. His confidence and ability to take charge in difficult situations would likely make him dominant.
Neither might be fully dominant. They could end up being equal partners. Sherlock's deductive reasoning and the Doctor's knowledge of the cosmos could complement each other so well that they work side by side. They would respect each other's abilities and share the decision - making process. For instance, in a case where an alien is using human technology to cause chaos, Sherlock would analyze the human part of the situation while the Doctor figures out the alien technology involved, and they would jointly come up with a solution without one being clearly in charge over the other.
It could be the Daleks. They are a classic Doctor Who villain. They might see the meeting of two Doctors as a threat to their plans for universal domination and try to stop it.
In this fanfic, neither might be more dominant. They could be equal partners. Harry Potter's immortality gives him the ability to endure many challenges, and his magic is a great asset. However, the Doctor has his own set of skills like being able to quickly analyze complex situations and having access to a wide range of alien technology. They would probably complement each other rather than one being dominant over the other. For example, when facing a threat that is both magical and technological, they would need to work together, with Harry using his magic to deal with the magical aspects and the Doctor using his technology to handle the technological parts.
They could also meet in a time - locked situation. The 12th Doctor is trying to solve a mystery from his past, and the 13th Doctor stumbles upon the same situation in her present. At first, they don't understand how they are both involved, but as they start to piece things together, they discover that it's all part of a much larger, more sinister plot. Along the way, they might meet some old friends or foes from their respective tenures as the Doctor. And in the end, they work together to outwit the mastermind behind the plot, all while having some really interesting conversations about their experiences as the Doctor.
In the fanfiction, the 11th doctor, with his eccentric and energetic personality, could initially be a bit confused by the 13th doctor's more modern approach. But then they could start to combine their wits. For example, the 11th doctor's knowledge of ancient alien races could be paired with the 13th doctor's understanding of current galactic politics. They could work together to save a planet that is on the brink of destruction due to a complex web of time - related issues. The encounter could also lead to some humorous moments, like when they argue about who has the better sonic screwdriver or who has had the more exciting adventures.
In fanfiction, when the 13th Doctor meets the 11th Doctor, there could be a lot of chaos and fun. They might exchange stories about their adventures. Maybe they would team up to fight a common enemy that spans across their different timelines.
One possible plot twist could be that they find out they are both parts of a larger plan by an unknown enemy. Maybe an ancient force has been manipulating their timelines to bring them together for some sinister purpose.
One possible plotline is that they meet in a time - locked situation. They have to work together to break the time lock. Another could be that they meet because of a shared enemy that has somehow found a way to target both of their timelines. They would then have to put aside their differences and use their individual strengths to defeat the enemy.