What eclecticsynergy said...
A given pickup might gain in openess when lowered, while another one will sound alive only when closer to the strings. It depends on the magnetic field involved, among other factors. That's why Bill Lawrence recommended a distance of "two nickels" (3.6mm) between wound strings and his L500's with ceramic mags while old Gibson docs mention a distance of 1,5mm only from strings to P.A.F. or P90's... Different strokes for different products.
Reason: BMT EQing won't necessarily change in the same way with different height settings according to the magnets at play - AlNi(Co), ceramic, neodymium...
"Compression" appears to me as a conceptual trap when it comes to pickups: some would say that lowering a pickup under strings "compresses" more its tone because it diminishes the harmonic content of transients... but our perception may differ : magnets being more or less sensitive to string excitation, they can change the speed/height of the attack for a given pickup. And a strong UNcompressed attack can ultimately "sound" compressed because it briefly overloads the first "host" in which the guitar is plugged (pedal or amp input, acting like a limiter because overloaded).
Rising or lowering the screw poles won't necessarily do the same if a pickup is covered or not. It won't even have the same effect if a pickup is asymetrically wound, or if the screws are made of an alloy with a different carbon content. :-/
Etc.
That being said...
-For "parallel" wiring (B+N in a LP, 2d or 4th positions in a Strat): carefully balanced volumes between pickups seems to give a more satisfying "qwack".
-Obviously, rising the screw poles of a humbucker makes the "South" coil louder. This coil being not at the same place for bridge and neck PU's, favoring it won't alter the tone in a same way - the boutique winder Zhangbucker sells a bridge "Slugbucker" whose "North" / slugs coil is wound hotter for more midrange and a neck "Woodbucker" based on the opposite recipe for more warmth with still a bit of sparkle... it suggests to set the screw poles down for the bridge pickup and up for the neck one, at least if the pickups are identical and symetrically wound... but again, this idea might be totally wrong with some transducers and guitars.
-Staggered poles are like screw poles protuding under the strings: they make them louder (and increase a bit the measured inductance, BTW). There's many web topics about unbalanced strings because of poles staggering - and about how to set pickups / screw poles under the strings according to the radius of the guitar... but a Gibson style HB or a Filter'Tron won't inspire the same advices on this question... and reliable sources may give really variable if not apparently opposite recommandations. ;-)
-A generalization that one should be authorized to trust (?) : rising a pickup progressively increases the harmonics comparatively to fundamental notes. IOW, it
should give a brighter sound to a given string (albeit setting the bass side of a pickup closer to the strings will still favor the bass, of course: these effects are not mutually exclusive, they are indicative of "timbre" vs frequency response).
-About non obvious strategies: in a totally counterintuitive way, the height settings of a pickup A affect the sound of pickup B even when pickup A is disabled: it's due to how the magnetism of pickup A interacts with vibrating strings.
No need to argue about all that stuff until the end of times, since experimenting to check my statements or other claims is easy: it requires only a soundcard, a frequency analyzer (there's many excellent freewares for that), a bit of time and a rational methodology.
And finally, IMHO, nothing is worth trials and errors, since the best settings for a pickup / guitar might be the worst for the next ones.
YMMV.
