You are completely correct of course, maybe my wording isn't right, but I essentially want to leave my amp settings closely matched and just change guitars to get that extra bit of grunt, I just want a slightly fatter, raunchier tone out of the tele straight out of the gate which I think is mainly the pickup and the winding. I have used some varied strat pickups and got wildly different results with similar amp settings: the SD hot rails sounded like fizz, Texas Specials just lacked any sort of sizzle with a bit of drive (to my ears), and settled on some Tonerider City Limits.
When I started putting higher gain into the equation they gave almost the opposite results.
The videos I had found online for Dimarzio in particuler were either dead clean and sounding the same, or they were high gain and not suitable for what I wanted.
Maybe you are right in that I just need to change amp settings and leave the pickup alone!! But I need one in any case, so I thought it prudent to find one more suitable to my needs.
Otherwise, why do we all spend thousands changing the pickup in our precision basses to get different results?? I have more experience in changing pickups on my basses rather than guitar and there are a HUGE amount of options out there.