From narutowiki:
Sharingan:
The first of the Sharingan's powers is being able to see the flow of chakra. The Sharingan can tell if a person is under a genjutsu because the person's chakra flow would be irregular. The Sharingan's second ability grants the user an incredible clarity of perception, allowing them to easily recognize genjutsu and different forms of chakra. This allows the user to pick up on subtle details, enabling them to read lip movements or mimic something like pencil movements or hand signs. As the Sharingan evolves, gaining more tomoe seals, this ability extends to being able to track fast-moving objects before finally giving some amount of predictive capabilities to the user. However, even though the user may be able to see an attack or know it is coming, their body may not have time to react.
The Sharingan's third and most well-known ability is that it grants the user the ability to memorize any technique that he or she witnesses, apart from other Kekkei Genkai techniques. The user can memorize ninjutsu, genjutsu, and taijutsu with near perfect accuracy, allowing the user to use the techniques as their own, or even modify them to create their own new techniques, much like Sasuke Uchiha's Lion Combo. In order to reproduce a copied jutsu, however, one must have the necessary skill or ability to perform them. A prime example is Rock Lee's brand of taijutsu. While Sasuke was able to copy some of Lee's moves, they put a much more significant strain on him since he hasn't trained nearly as much as Lee has. In addition to physical skill and kekkei genkai techniques, the Sharingan cannot reproduce jutsu dependent on other factors, such as summons that the user has not signed a contract with.
The Sharingan's final commonly-used ability is capable of inducing a unique brand of hypnosis that involves suggesting actions and thoughts to the opponent through genjutsu cast by simple eye contact.[5][6] More advanced Sharingan users can take the hypnosis ability even further to the point where a powerful summon like Manda or even the Nine-Tailed Fox may be controlled. When this was used against Manda and the Nine-Tailed Fox their eyes took on the tomoe pattern of the users' Sharingan while under hypnotic influence. The hypnotic ability coupled with the other aspects of the Sharingan, can make the user appear as if they can "see the future". First, the user must perfectly mimic every move their opponent makes and possibly their thoughts and words through careful observation. Then, they suggest an action to the opponent such as hand seals for a jutsu that the opponent and Sharingan user already know and copy that. With these things done, the user can complete the action even before the opponent does, possibly using the Sharingan's genjutsu to confuse or delay them. As with other genjutsu, genjutsu cast by the Sharingan are capable of putting an opponent to sleep, inducing paralysis, replaying memories to someone else, or creating various illusions to deceive someone. The potency of the Sharingan's illusion is dependent on the user's knowledge and skill with implementing genjutsu.
In addition to these commonly used techniques, the Sharingan allows the user to perform the genjutsu Izanagi. Using Izanagi, the user can warp reality for a short amount of time, changing reality into illusion and illusion into reality. However, this technique has been dubbed kinjutsu, because use of it causes the user to go blind.
Although the Sharingan consumes the user's chakra while active, the chakra levels that the user must exert is so insignificant that they can keep it active constantly. In fact, Itachi Uchiha was so masterful of it, he was able to keep it active for most of the time, only once deactivating it after using Tsukuyomi on Sasuke and Amaterasu to escape Jiraiya. However, when a Sharingan is transplanted to a non-Uchiha, the chakra drain is significant, leading them to cover it up when not in use, to stop the drain
Byakugan:
The first ability of the Byakugan gives the user a near 360º field of vision, except for one blind spot at the back of the neck above the third thoracic vertebra.
The second ability is being able to see through solid objects, and can use a degree of telescopic sight. The distance and the degree of telescopic sight varies from person to person, and can be improved. In Part I, Neji Hyūga was able to see an area of 50 meters, but later he increases his visual range to at least 800 meters, while Hinata Hyūga's range in Part II stretches at least as far as 10 km. However, the Byakugan cannot see through certain barriers, such as the Four Black Fog Battle Formation used by the Sound Four.
The third and one of the greatest uses of the Byakugan is the ability to see chakra, chakra flow as well as the chakra circulation system inside the body with great detail. It is from this particular ability that they are able to employ their ultimate attack style: Gentle Fist. Unlike the Strong Fist, which is focused on external injuries, the Gentle Fist style focuses on internal injuries. Each strike, when placed correctly, strikes along the chakra pathway system, which is the network of vessels that carry chakra. This network is closely intertwined with the functioning of the body's organs, and so, when the keirakukei take damage, the organs suffer as well. There is no defense against the Gentle Fist, since one cannot train one's internal organs to become stronger. The only possible defense is to stop the Gentle Fist's hits from connecting. Also, like the Sharingan and Rinnegan, the Byakugan's ability to see chakra and its flow allows the user to detect chakra sealed barriers.
Particularly skilled users of the Byakugan can take the Gentle Fist style one step further. Along the keirakurei are 361 pinprick-sized nodes called tenketsu, or chakra points. When struck, the Byakugan user can choose to either seal, or forcibly open these tenketsu, thus giving the user complete control over their opponent's chakra system. So, with precision, all those points along the victim's body can be sealed, stopping the chakra flow to those areas. Able to strike without force, and yet do more damage to a ninja than some of the most powerful ninjutsu, the Gentle Fist has been labeled as the greatest taijutsu style known in all of Konohagakure.
Byakugan is strong but I think the Sharingan is better evolved for battle. And the Uchiha clan members have powerful chakra, Hyūga Clan members chakra isnt special in any way. Hyūga Clan's Tijutsu may be the strongest but Uchiha would be able to predict every move. The Senju clan and the Uchiha clan were the two strongest clans in the world. And both Senju and Uchiha were the descendents of Sage of the Six Paths. It has been said that the Sharingan was somehow derived from the Hyūga clan's Byakugan but Madara said that the elder son inherited Sage of the Six Paths eyes so I think the Sharingan evolved from these and the the one(whoever he/she was, I dont remember) was wrong.
The Uchiha would wipe out the Hyūga.