Which strings on which bass?

I have a Gibson T-Bird with LaBella DTF's. Very dark, which is mostly fine since I'm not a big fan of really bright. Then I put Rotosound 66's on an old practice Peavy Fury and loved the mids I wasn't used to hearing. That somehow evolved into getting a new Am Std P, thinking it would be as good or better that the Fury. With the factory rounds it's frankly not (too sloppy and too much fret noise - I had to raise action quite a bit - I do have a heavy hand), so I'm ready to put the relatively new 66's on the Fender. But here's where I'd like some opinions - I see so much love for flats on a P on here that I'm wondering if it might be better to put the DTF's on the Fender for the deep thumpin, and move the 66's to the Thunderbird for the open 'woody' mid stuff. Kind of opposite from my original plan.