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Since the objective is to get our horses as light and as even on both sides as possible, all bits should feel the same on both sides of the mouth.  If you close the mouthpiece (of a snaffle) and one of the two ends (the butts) falls below the other, then the middle joint will sit off centre in the mouth.  The inside and outside curves of the branches or cannons should be the same.

Photo #519:  This unusual view of a KM D-Snaffle shows the offset Dees and how the mouthpiece should close evenly together, with each side virtually a mirror image of the other.  In this example, the mouthpiece is curved and tapered.