They may be better than diesel as a fuel but there is a clear link between the length of the carbon chain and the emissions of PM and NOx.
Methane as a fuel (CNG) is very clean as is propane (LPG), both cleaner than petrol. As the carbon chain lengthens so the NOx increases.
Part of this is due to increased combustion pressures and part is due to increased combustion temperatures.
It's all moot anyway. All new ICE engines will be banned in 15 years.
The NO and NO2 is a by-product of not the diesel or the long CH chain but the high temperature. Once you make your engine very efficient (using lean mixtures, oxygen surplus, etc, to gain the last 5% efficiency) AND inject fuel right into the pistons you starting to have extreme high peak burning temperatures which generate NOx. That is why the new petrols are having EGR and DPF and NOx convereters and the same king of soot problems. The legislation wanted to save us from 10-20% CO2 and gave us the misery of NOx.