I've gone to the aftermarket for all my Fender basses.
MIA Jazz four: Fralin noiseless Split Jazz
MIA Precision: Fralin
2008 Jazz V: Nordstrand NJ5FS purchased, but not installed yet.
For guitars, my 2004 SSS Strat has Lace Sensor Hot Golds. My 2001 HH Strat has its OEM pickups -- which are Seymour Duncans.
So none of my Fenders will have Fender pickups when my Jazz V gets its Nords. But for the Jazz basses, it was mostly to get rid of the noise. The stock Fender pickups sounded fine, especially in the Jazz V which sounds amazing. I also like the tone of Fender's American P-bass pickup, but on balance prefer the additional punch, clarity, and grit of the Fralin.