I don't know what's most effective AND economical between the studs - but denser is better.
But most effective would be using styrofoam panels behind the drywall to help reduce sound - not just because of its density but also because it breaks the contact between the studs and the drywall. Much of the sound that travels through walls travels through the materials, not through the air between the materials. If the drywall is separated from the studs, the vibrations will be lessened. You can soundproof the ceiling the same way, or by using firring strips to reduce the number of contact points between the drywall and the beams.