For several months I’ve had a P as well as my BB, and recently have been wondering if getting used to the sound of the P had been moving my tastes along a bit. In particular I seemed to be hearing a slight scoop in the BB tone that I hadn't detected before. And it's been bothering me.
And I've just realised that I've been taking the heavier right hand touch that the P has encouraged me to play with, and using it on the BB as well — and that's been wiping out the warmth of the BB's tone.
As soon as I told my fingers to think properly about which instrument they're playing, the balance of the BB tone came back.
When laid into, the BB (both pickups, GHS Boomers) starts to sound clangy, especially low down. When played with a gentle touch, the P (Dimarzio Model P, Fender 7250s) sounds insipid.