That's flattering, but I'm sure the kit timber would be judged by most to be of lower grade. The other significant determinant of sustain would be the neck fit which is fine for both. The Fender hardware is better quality, though the same basic design for both.
My input wasn't much more than making sure the screws were done up properly, which ought to apply to any bass.
Odd thing is the jazz has Fender roundwounds and the kit P had Fender flats. I would have expected the rounds to have more sustain.
I suppose the real question is why do some basses have less sustain? I suspect that in part its down to the pickups with the 'vintage' pickups in the Jazz being less sensitive.