What is stronger out of those three well depends what you mean by stronger really as they all have completley different abilties. It also depends a lot on which person actually has the dojutsu. for example Hinatas Bykugan vs Nejis Byakugan.
Rinnegan
The Rinnegan has been stated to be the most powerful of the three dojutsu which to me comfirns that it is the strngest of three Dojutsu. The Rinnegan can do many things such as when Rikudo Sennin the first person to have the Rinnegan created the moon or the Shinra Tensei that Pain used that has a huge destructive power and even the Samsara of Heavenly Life Technique which can bring people back to life and more.
Pain stated himself that his mastery of the Rinnegan was a lot less than Rikudo Sennin/Sage of the Six Paths, so potentially Pain still could have been stronger if he had trained even more on mastering his Rinnegan to its full potential.
Sharingan
The Sharingan can do many techniques things such as memorzing things or techniques so that they can be easily copied(depends how easy it is to copy depending on the user and the technique also the sharigan of course can not copy Kekkei Genkais).
Another thing the Sharigan can do is that it can perceive things much better than a normal eye it has the abilty to lip read, notice small things that most people dont notice or imtating exactlywhat somebody is doing.ANother abilty the sharigan has it that it can see the chakra flow of a person/people and can see anything is wrong with there chakara flow(for example when Kakashi saw that Rin was under Genjutsu). The Sharigan can also predict movements.
Another level of the Sharigan the Mangekou Sharigan can do extremely powerful Genjutsu and Ninjustu such as Amaterasu (Ninjutsu) and Tsukuyomi (Genjutsu)
Byakugan
The Bykagan can see nearly 360 degress (apart from from one blind spot) which makes it much harder for the person to be caught by surprise. Another abilty is that the Byakugan can see through objects (though there are some objects that the Byakugan can not see through).
Another abilty the Byakugan has is that it can see long distances away though the distance depends enitrely on the user(some people it is several metres and for some it can even be several Kilometres). Another important avilty is that the bykugan can see the chakra flow of a person and can also see all of the chakra points of a person.
The Gentle Fist is another ability that the a user with the byakugan can use which inflicts damge internal instead of externally. With the Gentle Fist the person can mainpulate there opponents chakra pointswhich can stop the person from using chakra completley and will also do damage to the internal organs(gentle fist is one of the strongest taijustu in the naruto world and is the most powerful in konoha). There are also many other power techques the byakugan can produce with (hard work or talent or a mixture of both).
Sharingan vs Byakugan/Comparison
The
Sharigan can
1.Copy movements/Techiques/Lip read
2.See the chakra flow, notice minor details (Not to the same extent as the Byakugan)
3.Predict Movements
Mangekyo Sharingan Abilties
4.Can do unique powerful Ninjutsu or Genjutsu (more powerful than the Bykugan techiques)
The
Byakugan can
1. It can see nearly 360 degrees
2.It can see the chakra flow,notice minor details ( much more than the sharingan and can see all the chakra points etc)
3.Can see through objects
4.Can see long distances (varies forom person to person)
5. Can use unique powerful techqiues (Not as powerful as the Mangekyo Sharingan)
So its personal opinon which one is stronger as they both are different and better in there own ways but in my opinon the sharigan is better in general. Kakashi said that the Byakugan has more perception and can see the chakra points etc than the Sharigan and not that it was more powerful.
What I think is the most powerful
1.Pain's Rinnegan
2.Itachi's Sharingan
3.Neji's Byakugan
Ive gone a little off topid here but o well

actually this has given me a thought for another thread havent made a thread yet. O and sorry if if i wrote down too much to read just trying to clear things up for people xD. My longest post on this forum yet didnt know i would type so much. i hope like my little rant thing xd