[FONT=Trebuchet MS][SIZE=1] Wow... really hard. It would mostly depend on the situation, but overall, Sharingan. Why, you ask...
The S. can copy attacks (duh). HOWEVER... B. can see through any copied attacks. The bad thing is that S. can't copy Taijutsu, so there's only a max of 66% mastery (if you completely conquered Nin and Genjutsu). B. can counter almost anything.
But as Kakashi proves, the S. is extremely useful for building up a vast stock of tons of different techniques, so that you don't just focus on one specific elements/medias, like Gaara's sand or Inuzuka's smell and tracking. If your defense proves useless, B. has nothing to fall back on. S. users usually have a huge number of different, well-rounded techniques.
The bad thing about S. is the strain on your body after using it. B. users don't experience it and can keep up a steady B. for days. The physical effects of S. are much more taxing and it takes longer to figure out how to use S. properly. B. is easier to get at first but doesn't have too many 'instant' bonuses like S. (copying jutsus, seeing through illusions). However, the B. has a huge number of techniques and edges that can stem from one simple attribute.
Geh... keep countering myself. Let's stop rambling at get to the point, shall we?
In my opinion, it depends on the situation. As Sasuke and Neji prove, both have weaknesses (albiet small) and both can be compromised in specific situations. It's practically impossible to simply state that one is better than the other. (We won't even delve into M. Sharingan because so few have it)
Bottom line? They both rock. Hard. [/FONT] [/SIZE]