Should I use acoustical insulation or acoustical drywall for interior walls?
If you're only going with one or the other, my personal opinion would be to go with accoustical drywall and seal the perimiter with accoustical caulk.  Insulation goes between the studs, so you could still have vibrations traveling through the studs themselves and the top and bottom of the wall's frame.  If you use sound-deadening drywall like QuietRock or use a double layer of regular drywall with Green Glue in the middle, you can avoid that flanking much easier since you're covering the entire area of the wall's frame.  Of course, worst-case sound situations could still allow sound to flank through the floor or ceiling, under or over the frame, and through the floor or ceiling of the neighboring room, but I'd think that would be an extreme case.