Not a Phat Phuk user, although I consistently drool over them daily and then talk myself out of it....
It just sounds like your pickup output. Some are just a hotter signal than others. Obviously your active instruments are going to be more output than the passive.
Heard really well here:
Fender TV Combos - YouTube
Watch until 5:14. You can hear how the output of the active hits the front end much harder than the passive, causing more extreme clipping.
The "phatter" response,
I'm guessing, is just due to the tonal frequencies normally produced by your bass. The Fender may have a wider tonal range than the Tobias (and hotter pickups), hence the difference in tonal reaction and clipping range.