Some of the examples in PAIP may be outdated in a historical but not practical sense. I've joked in the past that the code is so well-written than it can be excised and framed on a wall. With code this good, the lessons one can learn are numerous and the code stands the test of time.
Unfortunately, the same can not be said about the PCL examples since - to name two - there are far better ways to do binary parsing and pathname handling today than binary-types and cl-fad. The PCL examples are a product of the time that they were written but they are tied to a particular verbose, subjective style and were not "optimal" or even particularly good, back then.
Ultimately, PCL introduces Common Lisp to the audience as does PAIP. The difference is that reading PCL in 2020 will have minimum, let's say thought-provoking, impact. Reading PAIP (or Let over Lambda, SICP, On Lisp, Lisp in Small Pieces) remains -and will remain- a paradigm-shifting experience.
It does come together however, with some additional effort and extra passes.
Binary parsing depends on the application constraints.
You can't go wrong by studying Frode's binary-types (not the same as PCL binary-types) though [2].
I agree that the MP3 streaming server example in PCL looks outdated, but so are many topics in PAIP as Norvig himself points out at the end of his retrospective [1]. (And I still think that the MP3 parser in PCL is a really good example for showing Lisp I/O, binrary processing abilities, and subtleties of CLOS, despite not being something that anyone would code as a side project nowadays.)
[1]: http://norvig.com/Lisp-retro.html