Of the various dōjutsu in the Naruto world, the most notable are the "Three Great Dōjutsu ": the Byakugan, the Sharingan and the Rinnegan, eye-based abilities that grant the user different powers. Each one has its own characteristics that, when used properly, hold infinite possibilities.
The user has the incredible potential to produce a truly unparalleled level of power with just their eyes, but there are also a variable amount of other uses that make these dōjutsu are incredibly versatile as well. That being said, if a person somehow gained all three, which one would be best for regular duties to the village?
Byakugan
Most commonly associated with the Hyuga Clan, the Byakugan is a kekkei genkai that, unlike the Sharingan and Rinnegan, is present from the time of birth. As direct descendants of the Ōtsutsuki Clan, the Hyuga Clan inherited and have protected this coveted dōjutsu for generations for its unique properties. A Byakugan user gains a near 360-degree field of vision around themselves, save for a small blind spot at the back of the neck. It can also see through almost any object and over vast distances, as well as examine the human body and focus on the smallest insect in a vast forest. Additionally, the Byakugan has the ability to see chakra down to the chakra network, which is why the Gentle Fist style devised by the Hyūga Clan -- which attacks this network directly -- is their combat style of choice.
The Byakugan's ability to see chakra allows it to see through genjutsu but, unlike the Sharkingan, it provides no defense against it. Although it is present from birth, similar to the Sharingan, the Byakugan can typically only be awakened through intense training but there are instances like Himawari Uzumaki where users can unlock their eyes through instinct alone. That being said, users can expand the range of their Byakugan through discipline and training. Through a jutsu called Jukenkotai that only select Byakugan users are able to achieve, it also grants them teleportation, intangibility and stasis abilities that, when combined with the Byakugan’s field of vision, makes this dōjutsu extremely effective.
Sharingan
The dōjutsu of the Uchiha Clan, the Sharingan's powers originated from Kaguya Ōtsutsuki’s Rinne Sharingan, but its independent form was first manifested in Indra Ōtsutsuki. Unlike the Byakugan, the Sharingan only manifests in select members of the Uchiha clan and only as the result of experiencing powerful emotions with regards to their loved ones. Their brain then releases a special form of chakra that affects the optic nerve, transforming the eyes into the Sharingan. However, the trauma one faces awakening these eyes can be a double-edged sword. When first awakens, the user's enhanced perception is too fast for their body, causing them to overwork it to keep up with their new reaction time.
The three main abilities of the Sharingan are its enhanced kinetic vision, the ability to analyze and copy the structure of any movement or jutsu as well as powerful genjutsu. After experiencing more emotional trauma, the Mangekyo Sharingan is awakened creating a fully matured Sharingan, though the abilities of the Mangekyo vary between each eye. As each eye contains unique techniques, their abilities can range from the black flames of Amaterasu to the gigantic chakra avatar of Susanoo to Obito's multi-dimensional Kamui to powerful genjustu like Shisui's Kotoamatsukami. These powerful time-space manipulation and mind control abilities in both the real world and in the user's genjutsu world have untold applications.
Rinnegan
A Sharingan can also become a Rinnegan by obtaining Hagoromo Otsutsuki chakra, who was able to awaken his Rinnegan and Mangekyou Sharingan at the same time after almost killing his brother. The Rinnegan itself has the abilities of the Sharingan as well as all five basic nature transformations and the ability to create portals to other dimensions. Certain Rinnegan, like Momoshiki's, can absorb any ninjutsu and release it with amplified form, or they can be like Urashiki's, which lets him travel several seconds into the past. It also allows users to access the Six Paths Technique; the ability to manipulate attractive and repulsive forces, augment their body with machinery, read a person's mind while stealing their soul, multiple summons, absorbing chakra, calling on the King of Hell and even presiding over life and death.
The versatility and power of the "Three Great Dōjutsu " are unparalleled by any other, but their practical uses have untold possibilities as well. Ninja have fought and died for these ocular jutsu that were coveted for the uniqueness of their abilities. Each of the dōjutsu themselves have their own benefits that when combined together have endless potential. The Byakugan specializes in sensory perception so that is the best overall vision, but the kinetic vision and powerful genjutsu of the Sharingan, as well as space-time manipulation and Six Paths Technique of the Rinnegan, allow users to shape the world.
When it comes to day-to-day ninja work, the Rinnegan is without contest, holding the powers of the Sharingan, nature and life itself in its sights.