It's hard to describe because a) it changes more than one thing, and b) those changes are subtle. Note that this difference also applies to the difference between AlNiCo 2 and AlNiCo 5, a lot of what it said about AlNiCo 2 relates to pickups set lower, and vice versa. It's easy to say "brighter" or "darker", "harder" or "softer", but the change is makes is complex enough to defy simple description.I still struggle because there is conflicting information about pickup height and resultant tone ectetera.
When there is increased magnetic pull, the strings vibrate more asymmetrically, because the string is being attracted by a magnet on one side, but not the other. The waveform actually becomes more asymmetrical also, so if your gain is asymmetrical, it even changes the "bloom" character, or how the clipping changes as the strings ring out.
The asymmetry tends to increase higher harmonics, as if the magnet were gently causing a pinch harmonic in the location of the pickup. Therefore, the effect of pickup height will also vary depending on the location of the pickup.
Lastly, if the pickup is closer to the strings, the output is increased and the amp is pushed a little harder.
You can raise or lower the pickup one side at a time, making it more bass heavy or treble heavy, so the above would end up applying to some of the strings more than others. It's especially tricky with a Strat and its staggered pole pieces.