First off define "normal sharingan"
Then no.
If so then it is only because the user is better.
Give a sharingan to one person. And give a Byakugan to an exact clone of that person, and the sharingan will win.
The reason why is this, the Byakugan does not track movement like the sharingan. The sharingan also predicts movements.
Because of this, if someone were the exact same speed and had the exact same skill in taijutsu, the person with the sharingan would be able to see every attack coming at them beforehand and will have more time to react than the person with the Byakugan.
Secondly, there is no ability that comes directly from the Byakugan other than vision enhancements. All the Hyuga's jutsus aren't KG. Anyone can do them, it is just that the Byakugan makes it better. Anyone can put chakra into their fingers and hit people, it is just that the Hyuga knew where to hit and other people would be striking blindly, you see what I mean?
Back to my point. So if two exact clones fought, the sharingan user would always have the advantage. First off the sharingan can track high speed movement, can predict movement, and can copy moves also. Though copying wouldn't make a difference with exact equals, in a battle against someone else, they can copy a person's moves to better block and counter them.
Then the sharingan can cast genjutsu, whereas the Byakugan cannot.
So the Byakugan's advantage in this fight is that no one can sneak up on them, and hiding is useless. But against an exact equal with sharingan, they can't win. It is literally impossible.
So if a Byakugan beats a 3-tomoe sharingan it is because the user has more individual skill, not because the eye is more powerful.
The Byakugan isn't really a battle eye. It is better for scouting and tracking instead of direct battle.