Most of the usual arguments have been brought up. The lines between the two can two can be blurred a bit with judicious pickup choices. You can get thicker jazz tones with split coil pups or DiMarzio’s. Some genres of busy music like disco or funk will likely sound muddy with a Pbass, while rock or punk can benefit from the higher grunt of a split coil P bass. Personally, I enjoy having jazz basses, a classic 50’s split coil P bass and a single coil 50’s P bass. They all have their own window of tone.