It's a tough call, but it could be Light. If he manages to get his hands on the knowledge of the Inuyasha world and its rules, he could use the Death Note very effectively. He could target demons by learning their names, and since many demons in the Inuyasha world are vulnerable to human - like weaknesses in some ways, his strategic mind could make him a very powerful force. He could even manipulate some of the human characters in the Inuyasha world to do his bidding.
Inuyasha himself could also be very powerful in this crossover. His strength, speed, and his Tessaiga sword give him an edge. He has experience fighting all kinds of powerful foes. If he were to face someone like Light, he could use his physical abilities to overcome Light's reliance on the Death Note. Inuyasha could also potentially destroy the Death Note if he were to figure out what it was and its importance to Light.
One possible plot could be that Light Yagami discovers the existence of demons from the Inuyasha world. He might see them as a new type of 'evil' to be eradicated. He could start using the Death Note on demons, which would draw the attention of Inuyasha and his group. Inuyasha would initially be confused about these strange deaths and then realize that a human is causing them. This would lead to a conflict as Inuyasha believes in slaying demons in a more 'honorable' way and not through this strange notebook's power.
Sesshomaru could also be a very powerful character in this crossover. He has his own powerful sword, Bakusaiga, and his inhuman strength and speed. He is very experienced in combat against demons. Compared to Naruto's friends like Sakura, Sesshomaru would likely be much more powerful in terms of raw strength and combat ability. But Sakura has her own medical ninjutsu and superhuman strength when she releases her inner power, which could also be useful in different situations.
It's hard to say who would be the most powerful. Light has the power of the Death Note which can kill anyone directly. However, Lelouch has the Geass which can be used in very strategic ways to manipulate people. In a direct confrontation, if Light knew Lelouch's real name, he could write it in the Death Note. But if Lelouch could use his Geass on Light before that, he could make Light do things against his will.
It's hard to say for sure. Naruto in his Sage Mode or with the power of the Nine - Tails is extremely powerful. He has a vast amount of chakra and can perform powerful jutsus. However, Inuyasha with his Tessaiga, especially when it's in its upgraded forms, is also a force to be reckoned with. He has superhuman strength and speed, and the Tessaiga can cut through almost anything. But if we consider all aspects, Naruto might have an edge as he can use a wider variety of techniques and has more experience in large - scale battles.
In my opinion, Aizen could be one of the most powerful characters in such a crossover. His intelligence and his ability to manipulate others are already very dangerous in the Bleach universe. If he were to enter the Inuyasha world, he could easily use his wits to turn the different factions against each other. He could also potentially find a way to use the demon energy for his own gain. His Zanpakuto's powers are also very versatile and could give him an edge against the characters in Inuyasha's world.
If Naruto got the Death Note, it would be a complete chaos. Naruto has a strong sense of justice, but his understanding of it is very different from Light's in Death Note. He might initially be horrified by the power of the Death Note and try to destroy it. However, if he decided to use it, he could potentially target powerful enemies like Orochimaru or Pain without having to engage in direct combat. But this would also corrupt his ninja way as killing without a fair fight goes against his beliefs. He would likely struggle with the moral implications throughout the story.
The shinobi world's reaction would be complex. At first, there would be disbelief. Many would think it's some kind of new genjutsu or a hoax. But once they realize it's real, the more superstitious ninja would see it as a curse from the gods. The Hidden Sand Village might see it as a potential weapon against their enemies, while the Hidden Mist Village might be more cautious due to their history of bloodshed. The shinobi academies would start teaching about the Death Note as a new and dangerous threat. There would also be a black market for Death Note information, with some trying to sell false ways to protect against it.
One common theme is the clash of different worlds. For example, when L crosses over into a fantasy world, his scientific and logical mindset is at odds with the magic or other non - scientific elements of that world.
One main theme is the clash of different concepts of justice. In Bleach, the Shinigami have their own idea of maintaining the balance between the living and the dead, while in Death Note, Light Yagami tries to create a 'perfect world' through his own sense of justice using the Death Note.
In a Death Note and Naruto crossover fanfiction, Light Yagami might see Naruto as a threat to his new world order. He could use the Death Note to try and eliminate Naruto. But Naruto, with his quick reflexes and sage mode, might be able to sense something is wrong and avoid the Death Note's power. Also, characters like L from Death Note would be very intrigued by the ninja world's unique abilities and secrecy.