In the following video the guys from the YouTube channel Engineering Explained give and elaborate 4 reasons why the VR6 engines are slowly dying off. They give a comparison between the newest engine models and the VR6 engine. The first reason is nicely illustrated on a chart and the Atlas 2.0 turbo I4 cylinder is compared to our 3.6L VR6 engine, in which the torque curves are compared. The Atlas engine has a nice flat line in contrast to the VR6 which has just one peak point when the engine is most efficient and produces max torque, plus the peak torque is reached earlier with the Atlas 2.0 engine.
The second reason they discuss is efficiency. Namely they make a comparison between the 2005 VW GTI which has the 2.8L VR6 engine and the 2006 VW GTI which has the 2.0L I4 turbo engine. The VR6 has 200HP with 6200RPM versus the 200HP with 5100RPM on the 2.0L I4 turbo. At the peak torque at around 3200RPM on the VR6, the car weights 3036lbs and 1800-5000RPM on the 2.0L I4, the car weights 3308lbs. All of this leads to a conclusion that the new engine wastes around 9% less fuel. Check the video for more!
For more info about the VR6 engine, follow this link.