The main difference between the normal concrete and PQC is
PQC required low workability and placed directly without any means of like pumping.
Normal concrete in cases might required high slump due to pumping or due to high time required for placing.
PQC had low amount of fines as it wont require pumping.
Quality of the both concrete is good or better than it all depends on the how it is procured, produce, placed and cured.
PQC and NC is just a name or say formulation of product base on the desired requirement of each type of concrete, in terms of workability requirement, placing requirement, waiting time, strength requirement.
I see both as a concrete only which is produced for different applications.