How is it better? It can see better sure but it doesn't give any bonuses like being able to copy jutsu or predict movement, making taijutsu easy for a sharingan user. If you were to put up a sharingan user and Byakugan user together in a taijutsu fight then the sharingan user would win every time because the sharingan tracks movement easier, and predicts where the opponent is going to be.
The Byakugan does not give these bonuses, all of it's bonuses are only related to sight. The sharingan can copy almost anything perfectly, can track movement, can predict movement as well, and can see chakra, as well as cast some genjutsu.
The Byakugan has telescopic vision, 360 degree vision, x-ray vision, and like all the dojutsu can see chakra. It can also see when people are in genjutsu because of the chakra. It doesn't make them immune to genjutsu, nor can they see through everything.
So stack up the bonuses and compare them and tell me which you would rather have. Sharingan is by far more useful in a fight. The Byakugan is good for reconnaissance but it doesn't help too much in a fight other than being able to see the person's chakra pathway which doesn't help if you are not faster than the person you are fighting.
And to the person saying I am wrong about the sharingan predicting movement, please get out of here. Go reread the chapter where Sasuke finally gets his 3 tomoe against Naruto at the valley of the end. They show you how he can now keep up with Naruto's speed because while he may not be as fast his eye shows him where Naruto is going to go, something the Byakugan doesn't do. Don't get mad at me for how kishi wrote the story, I just accept it.