About 80% of people are right handed and 80% of those are co-dominant (right eye); the other 20% are cross-dominant (left eye). The reverse is true: about 20% of people are left handed with 80% of those co-dominant (left eye) and 20% cross dominant (right eye).
Of all the gazzillion of eyes I've looked at, I don't think there's much correlation between eye dominance and behavior, personality, etc.