I've owned the following Ps:
Sandberg California VS
Fenders: 1964, 1978/79, MIM 2005, MIM Classic 50s, MIM Roadworn 50s, 2016 CS relic, CS Dusty Hill gold top
Limelight
Bass Centre Bruce Thomas Profile
Vintage Tony Butler signature
...and have enjoyed them all. But it is the last two that I still own, because of the necks being just right for me. If I found another P with a perfect neck but dodgy pickup then I would happily swap out the pup and loom, e.g. for a Fender "Vintage P bass" or a Limelight if available.
So neck profile and fretwork are most important for me, plus of course weight.
The fact they were also the cheapest from that list is a bonus!