Shika is somewhat correct, the Hyuuga DO have that spinny thing( forgot what it was called ><) to block attacks from all directions. However, It seems as if the Sharingan and Byakugan were meant to cancel eachother out. Like someone said before, Imagine fighting yourself, except you counterpart has more Jutsus and a different bloodline. Even though the Byakugan is used to close the chakra holes( I know it starts with a T, but again, forgot what it was called ><) the sharingan is able to read movements, allowing the Uchiha to 'predict' movements. Statistically, The Hyuuga clan's bloodline is stronger, but, if two ninjas or equal calibur were pitted against one another( lets use Neji and Itachi as examples) the Uchiha would ultimatly win out. Only because, it would be practically, Neji fighting a taller version of himself that has WAY more jutsus, and forms handseals incredibly fast. The Sharingan is all about deception, with all the copying and such, while the Byakugan is about beating the crap out of someone's organs. In the end, it would most likely be a draw, but since the Uchiha has more knowledge with a variety of Jutsus, they could more than likely come up with a strategy faster, allowing them the win. (Now for my fan section of the post)
Personally, I like the Uchiha better, just because of the Sharingan's uber coolness. The Hyuuga clan is pretty cool and all, but I don't like the whole divided family thing...But, Hyuuga has Hinata and Neji, which gives the clan some significance.