This discussion about what chicken parts to compete with comes up regularly...and trends change.
Right now, if you want to win in KCBS or FBA you would be advised to cook thighs. I've had mixed boxes recently - the breast and thigh meat was good - but the white meat has NEVER yet (note: yet) come up to the moistness, tenderness, and flavor of the dark meat - if it's dry it's not going to score well. Lately I've seen more legs and the occassional wing box - the problem with legs is the thin bone end usually gets overdone to the point of disappearing and the boxes I've seen were definately overdone - the trick is to adjust your cooking methodology to the pieces you are cooking. The wings have suffered the same fate - I'm thinking most guys are cooking the wings on the kettle and they are getting a bit of the charbroil treatment - I love wings but can't score the ones I've been getting very high - dry, very dry!!
For you new guys - trust me, you have to learn that your personal preferences need to stay home...try something "different" if you wish but be prepared to spend time mf'ing the judges - I'm fortunate to be able to enjoy any piece of the chicken - but my turn in boxes, unless the trend changes, will always be thighs.
It has been mentioned that thighs "fit" the box better, though legs and wings make a nice box too. White meat has to be sliced or cut - there is no way you can get 6 or 8 white meat pieces in the box...extra handling, torn skin, shreds, etc.
Now, this is just my opinion - I'm not going to argue it one way or the other, but several thousand dollars and lots of crying in my beer has conviniced me to stick with thighs in competition.