I've been thinking a lot about this lately.
Have you ever heard a replacement pickup that made a P-bass sound like something else? A Jazz, a Rick, or maybe a an Ernie Ball MM?
Me neither.
Doing a pro setup, switching to a BT string set, and changing the tuners did far more to wake up my VMP5 than swapping the Squier pickup for an Am Std.
The more I think about it, the more I realize that as long as a pickup sounds balanced and doesn't hum, you're far better off working on the rest of your signal chain, or even better, your physical tone production.
Check out this vid: