As I said in my first post, it depends on the design involved... and even on individual pickups (!), as explained in the section 2 below.
Examples.
1-A DiMarzio Dual-Resonance is designed to have dissimilar coils - with the lower resistance coil being paradoxically the louder, since it has the same number of turns / same inductance than its neighbour...
Such a design has a good chance to sound different when the pickup is rotated in its cavity... albeit the goal of Dual-Resonance designs seems different from one DiMarzio model to the next: in fact, the Dual-Resonance principle appears to be applied to achieve almost
opposite effects, either symetrizing the response of coils beyond the main resonant peak and in loudness relatively to their position, either aggravating the comb filtering of high harmonics due to the unbalanced capacitive loads of 4-conductors cables.
2-A Bill Lawrence L500 has symetrical coils but still works with the unbalanced capacitive loads of its 4-conductors cable: depending on the remaining lenght of this 4-conductors cable and therefore, on the parasitic capacitance measured on each wire, it
can generate the same kind of dual-tuning effect than between unbalanced coils... In such a case, the symetrical coils of a L500 have been made randomly unbalanced by external means, so to speak, and the sound also changes when the whole PU is flipped...
Non limitative list, to be continued or not.