Having both a Touareg and a LR3 I will try to help a bit.
Mechically there not much of a comparison, the touareg is a better built car and has a more sports car like/driver feedback oriented response when driving where the LR3 is a bit more numb and heavy feeling. The LR3 handles more like a "truck" due to its setup and live rear axle. In the power department the treg also has the upper hand especially the newer ones with the FSI V8.
4WD systems on both vehicles are outstanding and can't say one is better then the other. A treg with air suspension is very similar to that of the LR3 in features and ride height. LR3 has a few more offroad settings.
Both cars have great interiors. I would say the treg has a bit better build quality while I like the LR3's better for its style. Where the LR3 really jumps ahead is in interior space.
I like both cars very much and for different reasons. I guess the best way to put it is the treg in V8 or diesel is more of a drivers car and the LR3 is more of a car for the passenger.
I would say the LR3 is better distance crusier do to the space and high comfortable seating positions, but my treg is a V10 TDI diesel with over 550 lb/ft of torque and gets nearly 30mpg on the highway