I've looked into sound reduction for some time. I will be renovating a condo that has "thin walls". There are now many products available to reduce the transmission of sound through walls and floors.
The answer is to isolate the vibration (energy) on one side of the wall from the other wall. Adding wool or fiberglass insulation is not the whole answer. You have a large piece of dry wall that will vibrate on wooden or metal studs and this will easily transmit the sound energy through the wall stud into the next room.
Stop the sound energy from being transferred to the other side by putting an acoustic mat under the drywall and limiting the number of fasteners holding the drywall. Two sheets of drywall will not work as the sound energy is transmitted easily.
Build two separate walls and isolate them so sound cannot be transmitted.
Another method is to use a system like IsoTrax which uses a special track attached to the studs and separates the drywall from the stud which reduces the transmission across the stud.
Google "How to reduce noise through apartment walls" and you will find many reasonable priced products and solutions.
Finally, the California department of health services has a study on effectiveness of various wall construction in the reduction of noise transmission. It is 175 pages with ratings of walls construction techniques. It is very technical but you will have some solid engineering work to base your decision.
Catalog of "STC and IIC Ratings for Wall and Floor/Ceiling Assemblies"
Russell B. DuPree
Office of Noise Control, California Department of Health Services
Berkeley, California 94704