Regarding the neck shapes - it’s not totally true about a bit of girth - the neck on my custom TT (not originally by me) is noticeably not chunky than a standard TT or any other configuration and is veering towards the old school P bass.
As far as pick ups go, all of them are great - no issues there for me from a Delano’s through sandberg, Haüssel, SD etc. As I have said in the appreciation thread - it depends what you want.
First and foremost it’s a bass comfortable to play/sit with/wear. Actually having a fairly ‘neutral’ sound can be of great benefit if it fits in with your tone shaping capacity/wants/needs.
Very Interesting about what @Opticaleye says about old vs new - would be really good to sit down side by side with similar models and have a tinkle