Jayne Cobb is A mercenary who didn't fight for either side in the Unification War, Jayne works for whoever pays him the best. At the moment, that's Mal, so that's where Jayne's loyalty lies — until something better comes along.
Major John Casey is as of this time now Colonel John Casey. He is an agent with the NSA in charge of protecting the Intersect, one Charles Bartowski. Casey was mentored by Ty Bennett, who taught him hand-to-hand combat techniques and attempted to help Casey, who already possessed a short temper, find a "calm center". He also attended Roan Montgomery's course on Infiltration and Inducement of Enemy Personnel and failed it twice – although it was revealed that Montgomery failed him because Casey's partner was "too pretty," with Montgomery also musing that he should have failed Casey a few more times on account of his attractive partner.
Who do YOU think should win?