I have three JMJs, but the bass sitting on a stand next to me at the moment is a Player (not the II version though) PJ mustang bass in Sienna sunburst with maple fingerboard. This bass is a lot of fun to play and offers a bit more tonal variety than the JMJs. I did do a fair amount of customisation to the PJ when I bought the bass secondhand at a very good price. This included shielding with adhesive copper tape and building a new loom with CTS pots, puretone socket, switchcraft switch and orangedrop capacitor. I also put on a Fender hi-mass bridge, hipshot HB10 lollipop tuners, and a fender thumbrest in the same position as on my JMJs. It currently has a set of short scale Ernie Ball cobalt flatwounds. The pickups sound good so I didn't consider changing them for something else.
The only changes I made to my JMJs was to apply copper shielding and put on some medium scale D'addario chromes.
The spaghetti logo on the player II looks wrong to me compared to 70s-looking logo on my original player looks wrong to me, but I tend to get irked by inconsequential things like that.
I don't know if Fender has improved how they wire up the player II mustang, but the circuit on the original player mustang bass annoyingly reduced the volume when rolling off the tone unless the volume was fully open. I used an alternative circuit when I rewired mine to prevent this from occurring. You can read about my adventures in rewiring here: