Hi Dan: fiberglas insulation will offer little in the way of sound deadening....except for high frequency. Usually, the sound transmitted between floors or walls is low to midrange frequency, which is where the power is. The longer wave length, lower frequency sounds strike the neighbor's wall (or teenagers floor above you), causing it to resonate at the lower frequency, and thus regenerating some of the waves on your side of the wall. I think your best bet is to do exactly as you are doing, but for mass and rigidity (which will resist the resonating wall's waves), I would use 2X4 studs, spaced so they are in between the existing wall studs, using 5/8" drywall on BOTH sides of the new wall. I would place the new wall about 1 1/2" away from the old wall, put the figerglass insulation (remove the foil or paper) on the outside of the old wall and then sandwich it between it and the new wall. This compressed fiberglas should help absorb most of the mid range while the mass of the new wall should block most of the low range.
This is a bit of guess work on my part, but seems like a logical approach. Hope it helps.