On one hand there is the general quality of the paint such as the formulation of the base, density and particle size of the pigment as well as the consistency of quality from one batch to the next.
There is also the pigment itself. Traditional pigments can vary hugely in price depending on the source and although there are inexpensive synthetic equivalents of any colour you might want specific pigments may be desirable for more subtle and specific qualities of transparency and luminosity. One example is real ultramarine which is made from ground lapis lazuli and is very expensive indeed, the dry pigment powder almost seems to glow in daylight.
More traditional pigments may also be desirable for reasons or historical authenticity or for reproducing specific techniques and effects. A lot of mineral pigments are metal oxides and may be toxic and so tend to be much more expensive to process and get hold of in the context of modern consumer safety regulations.
In practice this often comes down to how the pigment itself reflects light. Many oil painting techniques rely on building up many semi-transparent layers to achieve sophisticated lighting effects, especially for things like skin tones and atmospheric effects which you obviously can't do if the paint has a lot of opaque filler.