The nature of the insulation required is dependant upon the type of noise. Lightweight boarding will control high pitched noise but you need mass to deal with low pitched sound. What I would suggest is that battens are fixed to the party wall and a double layer of plaster board is fixed to that. This will give the weight needed to reduced the noise significantly. The gap around the edge of the new plasterboard needs to be filled completely. Also, make sure there are no accoustically weak areas. Check under floors, deal with any gaps - these can be a major source of transmission between properties.
Remember, whatever anybody says, adding weight is the only solution that and taking legal action.