For all intents and purposes I'm going to say a mastered byakugan is better than a mastered 3 tomoe sharingan:
1. The generic sharingan Genjutsu would be useless on the byakugan that can see through Genjutsu
2. The sharingan may allow you to perceive and copy your opponents moves, but only if the sharingan user in question has the physical ability necessary ( ie. an uchiha would have to have the water chakra nature to copy an opponents water style) naturally an uchiha likely isn't trained in gentle fist so naturally they won't be able to copy it.
3. The Sharingan may be able to anticipate an opponents movements but that only matters if the uchiha in question is either near equal, equal, or greater in speed than the hyuga in question which I doubt.
4. I believe that the hyuga are likely faster, stronger, etc. because of their specialized combat, the gentle fist requires a lot of taijutsu training which I believe makes them physically superior to most normal shinobi including your average uchiha whose skill primarily typically varies whereas a hyuga it's certainly is skilled in taijutsu due to the requiems of their chosen style.
While the Sharingan certainly has its advantages they are very specific and dependent on the physical capabilities of the uchiha in question, if he is not capable of keeping up with the hyuga in question then his sharingan is ultimately useless, additionally the byakugan has better range, focus, and novelty compared to a regular sharingan.