apias:
There's really a very simple experiment that can be performed to test this; you don't even have to drive anywhere and no expensive instruments are required. You can perform this test with either a petrol or diesel engine, the results will be the same.
First, with your car in the driveway, facing upwind, get in the car, start the engine, close the windows and turn on the ventilation system to draw air in from the outside. Do this for 30 minutes and note how you feel breathing this air being "breathed into" the car.
Now, shut off the ventilation system, turn off the engine, connect a hose to an exhaust pipe and run the hose into the car through one of the windows, partially opened, tape some plastic over the window opening to seal it and make sure any other windows are closed. Get in the car, start the engine, make sure the ventilation system is off. Do this for 30 minutes and note how you feel breathing this air coming from the exhaust.
In the unlikely event you are still alive after this second trial, compare your impressions of the air quality, and let us know which you feel is "cleaner".
The carbon monoxide levels emitted by all modern cars today is so low, a half-hour run isn't going to do much beyond giving the occupants a slight headache and, perhaps, some smelly clothes. It will take much longer for carbon monoxide to become effective.
Returning to the subject of Volkswagen and illegal emissions, while Volkswagen did break the Clean Air Act and should be suitably punished, the tirades one often reads do little to accomplish that goal. The emissions are magnitudes lower than many other vehicles in operation throughout the world and agriculture, and one's lawn, emit significantly higher levels of nitrous oxide compounds annually.
Volkswagen is not alone with gaming the emission standards, though most other automakers are not as blatant; however, consider hybrid powertrains, especially plug-in hybrids. The operation of these prime movers fit the very definition of cheater devices as set forth against Volkswagen by the EPA and CARB.