Dips and chins are not antagonist exercises. The torso muscle activation for both exercises is similar, with the exception of the deltoids (rear for pullups versus anterior for dips). The main difference is that pullups strain the biceps/brachialis/grip, and dips strain the triceps. I think if your brachialis and biceps are as strong as your triceps, THEN you have to start worrying about imbalances.
These exercises tend to be lumped together because of their reliance on bodyweight as opposed to any physiological reasons. A more appropriate antagonist exercise for pullups would be military presses. A good antagonist exercise for dips (to the extent that there even is one) would be cleans or perhaps shrugs.
I would be interested in the appropriate ratio between dips and pullups though.