The J pickup would be noisy, for a start. Otherwise I’m not sure there would be a great deal of difference; after all a split P pickup is basically a J pickup cut in half....
Thats before you start looking at how different pickups of the same type sound, but in principle, similar.
For example G&L used a single jail ‘Jazz’ shape pickup in their early P bass types. Being an MFD pickup it was extremely high output so whilst a single coil is noisy, the signal to noise ratio was ok, however it was later split into a humbucking type.