From what I remember of the descriptions of the Sharingan and the Byakugan, sepcifically from what Kakashi said to Sakura, is that the Byakugan is superior in terms of INSIGHT, not superior over-all. We should remember that only the Sharingan can copy movements and retain them in memory, the Byakugan cannot.

Both have their advantages and disadvantages. Also, I was under the impression that the reason why Kakashi got worn out when he used his Sharingan is because he wasn't bornwith it (right), while Sasuke was? Not only that, but we have not seen a Ninja born with this ability REALLY use it; while Neji had the benefit of realizing his ability sooner.