Wait a minute: the amount of information in a typical Jazz chart is vastly inferior compared to the information typically found in a score for a classical piece. This is because in Jazz, much more is left to the discretion of the musicians. So, it is quite difficult to correctly compare the two, since they don't have the same uses.
About the double sharp, it often has to do with tonality. Classical music is typically more tonal than jazz. The sharp is needed when you temporarily change tonality, and some tonalities just need double sharps then and there –Gsharp dur for instance. If you wrote the natural note instead, it would not convey the intended tonality.