The trim pots don't change harmonic content, only the amount of signal being sent to your rig. As Adam alluded to, where it makes a difference is your rig's ability to handle that much signal. Personally, I have my trim pots turned all the way up, as I want to send as much signal as possible at the beginning of the chain to keep noise levels down. And I tend to think it helps with tube saturation, though I could be wrong about that. And as Adam said, the 10db difference in the two inputs on the F-1X can make a significant difference.
On pickup height, I tend to think that the closer the pickups are to the string, the more growl; the further away the pickups are from the string, the cleaner the sound. But I don't know how significant the difference is; my pickup heights are based primarily on playing comfort.