My poor little 2002 went to VW recently for the coil pack recall. Ran like a top when I took it in. They replaced the coil packs, and I got the car back and drove home. Next day, when I started it up, it did exactly the same thing as yours. Sputtered, missed, chugged, etc. But it would usually start doing this after you warmed it up.
It turned out that somehow , VW managed to break the Mass airflow sensor and the throttle body. Not sure HOW, but they did.
They replaced the Mass Air Flow Sensor first, and that seems to have fixed a majority of the problem, then they also cleaned the throttle body and put it back in. No more chugging or loss of power.