Okay, if you kept everything else the same, particularly the number of turns and the overall coil geometry, and you just changed from 42 to 44 awg wire, you could expect:
1.) The output level would go up a little bit, due to the increased DCR, which loads the amp a little more.
2.) The resonant peak would be lowered somewhat, reducing the highs and boosting the high-mids.
However, these would both be small changes. The difference in DCR, impedance, and capacitance if only the wire gauge were changed, wouldn't be very much.
Much larger shifts in the tone curve will come from changing the number of turns, and/or the shape and position of the wires in relation to the magnetic field.
When I develop new pickups for my basses, I usually start out with a target for the DCR and number of turns, based on the wire that I want to use. That, combined with the magnet size and strength I've chosen, establishes the output level (power) and amp loading for the design. Then I play around with the coil height, bobbin thickness, layering, etc., shifting the wires around in relation to the magnetic field, to shape the tone curve the way that I want it.
But that's just how I do it. As I said before, pickup design is a complex problem with many interconnected factors. There are different ways to approach it, to work towards a particular result. Two pickups can be quite different in "recipe" and end up with the same tone.