Here's a picture of how high my pickups are and how close they are to the strings.
View attachment 3967972
Granted, I have my neck shimmed, so the saddles are a bit high off the body, but still the bridge pickup is about 2 mm from the strings, and the neck pickup is 3 mm away. I fiddled with them until I found a distance that gave me a nice throaty sound where each pickup was audibly giving the same output.
BTW - that thing between the pickups is a thumbrest. After I readjusted things shim-wise I need to make a taller one.
The only reason I could think of for the difference in output between active and passive preamp setting would be a need for a new battery. There's no difference on mine with a new battery. The pickups themselves are passive and the preamp is active.