Anti roll bars, or sway bars, limit the roll of a vehicle by making both wheels at one end of the car move together. The thicker the anti roll bar the more pronounced the effect.
The reason people see great benefit from fitting a thick rear sway bar is that holding the rear of the car level also holds the front level.
However... there are down sides to controlling roll with just sway bars.
First, you start getting unfortunate single sided bump responses, your left front wheel goes over a bump and your right front lifts too. Not good.
Second, if you stiffen the rear but not the front the front remains compliant but the rear does not. What's that mean? Well it means you get very large weight transfers to the outside rear tire during cornering, there comes a point where you exceed the limit of adhesion for that one tire and, since the inside rear tire has been unloaded, you go into a dramatic oversteer. That is to say you spin and head for the scenery.
In general it is a bad idea to make drastic changes to one end of the car. Some people take off the rear sway bar in wet or winter weather.
You can also limit roll by simply fitting stiffer springs. Though it's a lot harder to fit springs than to change sway bars.
The Passat already has a rear anti-roll bar, all the Neuspeed bar does is stiffen the torsion beam axle which is just a big sway bar with the wheels mounted on the ends.
Read the discussion on the "Shine" suspension in the technical->suspension section of the vwvortex.com forums, there's a lot of good information there. It may be standard to fit the huge rear sway bar, but it's an ill informed choice.
Drastic lowering is also questionable for handling, it can push the front suspension out of its semi-linear range and that means you get nasty bump steer effects. Part of the reason you get understeer in modern cars is that as the suspension compresses on the outside front wheel it turns the wheel out slightly. This gives you the feeling of understeer but without reaching the adhesion limits of the car, so it's understeering but you aren't anywhere near the limit of your ability to turn.
That brings us to another nasty concomitant effect: if you switch off the roll induced understeer by stiffening the car then when it does reach the limits it's very sudden and you have correspondingly reduced chance of surviving the experience.
[edit]
Oops, that should probably have been the McPherson thread
http://forums.vwvortex.com/zerothread?id=1363022
A great many illustrations have been added since I last read that thread, either that or I read it at work and we block his photo host.