In modern usage, there is little difference between them, although the 'on' version is vastly more common. Originally, going back centuries, there was a difference. 'On behalf of' meant 'as a representative of', as in "I am speaking on behalf of my wife"...ie because she cannot be present. 'In behalf of' meant 'in the name of', as in "(They) rob in the behalf of charity" (Shakespeare)...ie for the benefit of.