They're both useful for different tasks.
Byakugan is best suited for reconnaissance and tracking, with it's ability to see long distances through solid matter. In combat, it does have usefulness as far as being able to see nearly 360 degrees, as to avoid surprise attacks. However, in actual combat, it's really only good with the Hyuuga Gentle Fist style of combat using it to pinpoint the particular weak spots.
Sharingan, on the other hand, is more suited to combat. Being able to read your opponent's movements and understand them accurately is important in battle. Unlike the Byakugan, the Sharingan also possesses an offensive form in the Mangekyou genjutsu. The Byakugan, to my knowledge, does not possess any offensive qualities.
If I recall correctly, the Sharingan is actually sort of a genetic offshoot of the Byakugan, and they were originally from the same family...meaning that the Uchihas and the Hyuugas are probably distantly related.