How much worse is the typical subway air, compared to street-level air pollution, in a typical city?
Depends on what type of pollution you are talking about

Moreno et al., 2015 studied this problem in Barcelona, and compared Metro (subway) to trams, buses, and walking in various parts of the city. There is a massive overabundance of data in this paper that mostly speaks for itself, but let me summarize.

The subway was in first place or last place in most measures; it was the only system that didn't occupy the environment of the city streets. So these comparisons are probably exactly what you are looking for. Subway air had the lowest count of particulate matter, and the highest modal particle size; both of these are good. However, at the same time, the PM$_{2.5}$ (fine particulates which are particularly dangerous carcinogens) for subway and bus were notably higher than for tram and walking. 

The black carbon levels were in the middle of the road; lower than for pedestrians but higher than bus or tram. However, the authors note that black carbon may have been overestimated for the subways; so these levels could have been lower.

Carbon monoxide is largely related to combustion engine usage; CO levels were lowest on the electric trams, and higher on the other modes of transportation. Carbon Dioxide, on the other hand, is largely related to other passengers breathing; CO$_2$ was highest on the crowded vehicles and much lower for pedestrians. CO$_2$, unlike the others, I don't think is a chronic health risk at the observed concentrations.

Conclusion

There is a lot of information in that paper, and I am not really qualified to judge the health risks from one factor against another. I can note that in no health measures does the subway have the worst air quality between the four transportation modes; and there is no other mode that has better air quality than the subway in all measures.

I suppose it is safest to say that, in a statistical sense across multiple measures, the subway air is not significantly more unhealthy than street level air.