Re: Dual Resonance vs Asymmetric Wind
Even without coil-tapping, having mismatched coils will make a tonal difference, and to many people's ears, and improvement.
By making one coil (usually the crew coil,) stronger, you gain more trebles and clarity. It's also making it a bit closer to a single-coil. It's great for cleans, light overdrive and for getting a "true" PAF tone, (which were usually would unevenly because they didn't have accurate counters.)
The down side it, because you're making one coil stronger, you also will induce more hum and noise than a 'bucker with perfectly matched coils.
Matched coils will usually give a fatter, rounder sound with a softer attack.
And as far as coil-splitting, having one stronger coil will make for a louder, more accurate single-coil sound when tapped.
A side benefit of asymmetrically wound coils is that you can flip the pickups, so that the screws face either headstock or bridge, and hear quite a noticeable difference in tone. It's great for fine-tuning, and you can make your neck pickup position have more clarity and treble, or your bridge be a bit loud, warmer and fatter.
It's all about what preference you have as far as your tone. Personally, I really love asymmetrically wound coils, but then I don't use much distortion.
Good luck!