I took the PhD quals when I was in grad school and can say, at least at my school, that they were very broad within my disclipine.
However, I wouldn't want to rely on the quals as a proxy for the PE exam, because they are not standardized across the country like the NCEES exams are. So how could you say for sure each school's quals met the standard for "minimally competent"? You'd pretty much be relying on the faculty of each college to determine "minimally competent," rather than whatever process NCEES uses--which I imagine is a bit more rigorous (though I could be wrong).
However, I wouldn't want to rely on the quals as a proxy for the PE exam, because they are not standardized across the country like the NCEES exams are. So how could you say for sure each school's quals met the standard for "minimally competent"? You'd pretty much be relying on the faculty of each college to determine "minimally competent," rather than whatever process NCEES uses--which I imagine is a bit more rigorous (though I could be wrong).