Well, it's really tough to say. Annabeth is extremely intelligent in the world of Greek mythology. She's strategic and has a great understanding of ancient knowledge. But Hermione is no slouch either. She's book - smart and has a vast knowledge of magic. In a fanfiction - based battle of wits, it could go either way depending on how the author writes it. Maybe if it's in a magical setting, Hermione might have the upper hand because she can use magic to her advantage. But if it's in a more traditional problem - solving situation, Annabeth could shine.
I think Annabeth has a good chance. She has a very practical kind of intelligence. She's used to dealing with life - or - death situations in the world of demigods. In fanfiction, if the situation is more about survival skills and using the environment, Annabeth could be the winner. She can analyze a situation quickly and come up with a plan. Hermione is brilliant in her own world of magic, but outside of that, Annabeth's street - smartness and strategic thinking could give her the victory.
Hermione would probably win. She has been through so many life - threatening situations in the wizarding world and has always managed to come out on top with her quick thinking and vast knowledge of spells and magic lore. Annabeth is smart too, especially when it comes to Greek mythology and strategy, but Hermione's ability to adapt and use magic gives her an edge. In fanfiction, there might be some scenarios where Annabeth could hold her own, but overall, Hermione seems more likely to come out victorious.