Why do some oral surgeons wire a jaw shut and other rubber band them after double jaw surgery?

This is a great question. In general it depends on how well the plates hold the bones together. In my practice we will usually place rubber band and try to plan for the plates and screws to be placed in strong bone. 

There is no reason at all to wire jaws anymore. Elastics are also a bit of overkill since the new techniques (20 years + in existence) fix the bones back together with pins/screws/plates. Therefore the jaws are 'solid' unless special circumstance. The surgeon has to be comfortable with his experience and approach however.