The P vs P/J thread is a frequent visitor to TB and it's never conclusive. But I love it because, even though the argument is never resolved, we always get such great bass porn!
As for P, J and P/J, I confess I only only have a J and a P/J (pics of two of them below), but mine are fretless so they don't really sound at all like a typical jazz or precision bass so there isn't a basis for comparison to the original situation even if I did have a pure P bass.
But as for the specific sub topic of P vs P/J, my experience is that, all else being equal, it's going to be very difficult, if not impossible to really detect the difference between a P with the split-coil soloed vs a pure P. In a blind test I doubt anyone would really be able to do it. With the bridge PU turned down, you have a 250Kohm resistor in line with the pickup so, while it's not fully out of the circuit, it's effectively out of the circuit.
That said, I like the way the tony franklin does it, with the big ol honking blade switch like on a guitar. That takes the jazz pickup completely out of the circuit (as far as I know), so in the P position it's a "pure" precision bass.
The other thing I will say is my tony franklin is the first bass I've ever owned where I regularly use the neck pickup. I've always had 2 pickup basses, but that's because I could never get those basses with just the bridge pickup. I always had to buy the 2 pickup version and just always leave the switch on the bridge PU.
I know that's weird, but I actually use the switch on the tony franklin. Even my jaco I never use the neck PU - just the bridge PU.
That's how I knew the tony franklin was a keeper and just your run of the mill bass

. And if I get a fretted precision bass at some point, it'll be a P/J....
L
View attachment 3972289
View attachment 3972294