All engines have to draw in a given amount of air through a filter. The more free-flowing the filter, the less work will have to be done to get the air in. Regardless of what happens inside the engine. A turbo diesel will be drawing in much more air than the displacement of the engine because of the pressure increase, but then again the engine will be running at lower revs overall, so that would even things out with respect to a NA petrol… hmm…
Interestingly, drawing in warm air into a petrol engine can increase MPG significantly.
With regards the petrol/diesel argument above – both types of fuel need both more air AND more fuel to produce more power. One is useless without the other. A modern petrol will refuse to inject more fuel if there’s not enough air to burn it (which is why you lose power at altitude).
In a petrol car if there is not enough air to burn the fuel the ECU can tell because there is more of something in the exhaust.. CO perhaps? However in a diesel you just get smoke, and the ECU can’t detect that. However a turbo diesel can detect how much air is coming in so it can increase the turbo boost (assuming a modern VNT turbo) to maintain the amount of air it needs. Same is true for a turbo petrol.
HOWEVER if the air intake was restricted, then the ECU would have to make the turbo work harder, so that would in turn restrict the outflow of the engine reducing power and economy very slightly.