Perhaps this different Sharingan has the power to control the elements in a completely new way. Instead of just the basic fire, water, etc., it could combine them in unheard - of ways. For example, creating a storm of ice and fire simultaneously. This would give Naruto a huge advantage in battles and also make for some really cool fight scenes in the fanfiction.
One possibility is that this Sharingan can communicate with other dimensions. Naruto could use it to seek help or knowledge from other realms. This would open up a whole new world of allies and enemies. He might even be able to bring in powerful beings from other dimensions to fight alongside him or learn new jutsu from them.
Well, it could have the ability to time - travel. Imagine Naruto using it to go back in time to prevent some of the great tragedies in the Naruto world, like the Uchiha massacre. This would change the whole storyline in a very interesting way.
His relationship with Sasuke would be very different. Since the Sharingan is an Uchiha - related thing, Sasuke might be both jealous and intrigued. They could end up being rivals in a whole new sense, competing to see who can master their respective powers better.
In fanfiction, Naruto could get the Sharingan through a blood - related connection that is revealed later. For example, it could be discovered that he has some distant Uchiha ancestry that gets activated somehow. Maybe a powerful enemy's attack awakens this dormant Uchiha blood in him, and as a result, he develops the Sharingan. It could also be that a powerful sage or a new character uses their own unique powers to bestow the Sharingan upon Naruto for a specific purpose.
One drawback could be the strain on his body. The Sharingan is a powerful dojutsu, and Naruto's body, which is used to his own chakra system, might not be able to handle it well at first. This could lead to fatigue and over - exertion during battles.
A character with both Mokuton and Sharingan would be unique in terms of combat style. They could use the Sharingan to predict an opponent's moves and then quickly use the Mokuton to create barriers or offensive wooden constructs. For example, they could see an incoming attack with the Sharingan and immediately grow a wall of thick trees with the Mokuton to block it.
One possible plot could be that Naruto discovers he has the ultimate Sharingan through some mysterious means. Maybe it was a hidden power passed down in his family that was dormant until a certain event triggered it. Then he has to learn to control this new power while still using his own unique ninja skills.
One implication could be enhanced power. The Sharingan already has powerful abilities like seeing chakra flow and predicting movements. A golden Sharingan might have even more advanced or unique powers. Maybe Naruto could use it to see into the future more accurately or manipulate chakra in a completely new way.
Sakura could be an unexpected character to have the Sharingan. It would completely change her character dynamics. She could use it to enhance her medical ninjutsu, seeing the internal body structure more clearly. Also, she could become a more formidable fighter, using Sharingan - based genjutsu to her advantage.
One unique feature is the combination of two very different power systems. The sharingan with its abilities like genjutsu, and the Avatar's bending powers. It creates a whole new set of possibilities for combat and character development. For example, a character might use the sharingan to predict an opponent's bending moves.
Well, in fanfiction, anything can happen. Maybe it could be due to some secret experiment. Some fanfic writers might create a scenario where Orochimaru, known for his unethical experiments, somehow implants the Sharingan into Naruto. It could also be a result of some strange jutsu gone wrong that links Naruto to the Sharingan in an unexpected way.
His character development would likely be more centered around the power and mystery of the Sharingan. He might become more brooding and introspective like Sasuke at times, as he tries to understand the power he has been given.