Well, NOx is more soluble, eventually. It's a bit more complicated, in that it has to do a few reactions first.
2NO2 + H2O --> HNO3 + HNO2
The HNO3 (nitric acid) is completely miscible with water - they'll mix in any proportions. So that goes away quickly. The HNO2 (nitrous acid), on the other hand, is unstable and breaks down to a combination of nitric acid and nitric oxide:
3HNO2 --> HNO3 + 2NO
So, that's another one NOx gone as nitric acid, but those nitric oxides have to undergo one further reaction:
4NO2 + 2H2O + O2 --> 4HNO3
So, it all eventually turns into very highly soluble nitric acid, but I'm unsure of the rate at which this happens.
SO2 is relatively straightforward. It dissolves in water to around 200g/kg (a very high concentration, meaning that it really does like to be in water) at low temperatures, where it will react with water and oxygen to produce sulfuric acid:
2SO2 + 2H2O + O2 --> 2H2SO4
H2SO4 (sulfuric acid) loves water. So much so, that an old-school chem lab method for pulling the moisture out of a vacuum desiccator is to put a pool of sulfuric acid at the bottom.
So SO2 scrubs out very quickly as long as it hits atmospheric moisture (under very dry conditions it will of course last longer). NOx is a little slower, but still disappears quite quickly in the grand scheme of things.
That's my understanding, at least. Not really in the mood for going digging for precise rates.
