Obviously you have not read too many, if any, case studies into the matter Dan.
Left handers tend to be more emotional, higher self-confidence, prone to personality quirks, creative, artistic, empathetic, quicker learners, unpredictable, inductive, intuitive, abstract thinkers, geometric orientation, visual accuity, visual adaptibility, spatial sense, affectionate, and kind hearted.
Right handers tend to be more logical, lower self-esteem, dull, refine more than create, sympathetic, studiers, predictble, deductive, "reverse" thinking (by this I mean look to the past to think of how it affects the future),concrete thinking, algebra oriented, weaker eyes, worse night vision, temporal sense, cold, and more likely to see others as lessers.