In such a fanfiction, there might be a big threat that requires both teams to combine their skills. The Flash could race with Kid Flash and share some speed - related tips. And Wonder Woman could train the female members of Young Justice in combat.
They might be really surprised. Some fanfictions could show their characters in very different ways than they expect. For example, they might see relationships between characters that they never thought of in the official story. It could be both amusing and a bit strange for them.
Batman is often a very popular character. In fanfiction, he can be portrayed in different ways, like a more nurturing mentor figure to the Young Justice team or as a master strategist leading the Justice League in complex battles.
Some of them might be amused. They could find the different takes on their characters and stories quite entertaining. For example, Superman might chuckle at a fanfic that has him in a comical situation.
A third interesting storyline might involve a secret alliance between a member of the Justice League and a villain that the Young Justice team discovers. This discovery then sets off a chain of events where the Young Justice team has to decide whether to trust the rest of the Justice League and how to handle this new information without causing a complete breakdown in the superhero community.
Superboy is often a popular choice. His complex origin story, being a clone of Superman, gives a lot of room for exploration in fanfiction. Writers can delve into his identity issues and how he fits in with both the Young Justice team and in relation to the Justice League.
Maybe a story where some of the younger members of the Young Justice team are frustrated with the Justice League's methods and decide to take on a mission on their own, but end up getting in over their heads and have to call in the League for help. This could lead to a lot of character development and some interesting dynamics between the two groups.
One idea could be a misunderstanding that leads to a fight. Maybe the Justice League mistakes some of Young Justice's actions as being too reckless and end up in a battle. Then they realize they were wrong when a real threat emerges and they have to work together.
One idea could be that the Young Justice team has to prove themselves to the Justice League during a major alien invasion. The League initially doubts their abilities but as the battle progresses, they see the unique skills and teamwork of the young heroes.