I have been lucky enough to play quite a few PAF equipped guitars including a couple bursts and the reality is...they were ALL different. Of the 7 or so guitars I've played, the one commonality between them is that yes they are generally brighter, but a warm bright and not a brittle bright. I don't usually like subjective terms like "round" or "chewy" to describe tones, but they certainly fit the bill. Sounded like really great single coils with more midrange heft. Really nice compression/sag feel to them even playing bone dry clean. (yes i know sag is most commonly used to describe the rectifier/output stage of a tube amp but it's the best word i've got at the moment)
I still try to understand what pickup makers like to describe as "bloom". That term has eluded me, I could very well have experienced it but nothing much to write home about from my pov anyway, other than that they were all great pickups but nothing over the top magical that great modern repros (like Virgil Arlo, TS Bloombuckers, etc) can't replicate fairly easily and inexpensively (compared to vintage anyway). Neck pickups I think are where vintage PAFs really stand out in comparison, they are so much clearer than any modern pickup I've ever played, even the top dollar replicas.