Why “direct” PostScript makes sense 15 years ago
PDF is typically directly generated these days. There's no need to generate it from PostScript first.
The main difference between the two is that PDF is a declarative definition of the page whereas PostScript is a turing complete language. You can write a PostScript ray-tracer which will execute on the printer itself something which would never be possible in PDF. On the flip side, PDF is far more efficient as an electronic document format.