It's a little worse than that.

After Dieselgate, Volkswagen brought their diesels into compliance by software patch. People did dyno runs of all VWs before and after the patch, and in many cases (e.g. the 180HP Passat) got something like 10% less horsepower and drastically worse torque curves (max torque at 1900 rpm instead of at 1500 rpm) after the patch. Fuel economy also went down by around 10% because of the patch.

Makes sense from a thermodynamic perspective: your engine runs with more power/torque and more efficient if you run it hotter. But running a diesel hotter makes much more NOx.