I expect this has an even bigger impact when there's only one pole per string.
I've been mulling this issue for an upcoming single-coil Precision bass build. Numerous pickups are available for that, both in traditional 3/16" pole width and the wider 1/4".
I asked Larry at Aero about the difference between the models he offers. Here's the "meat" from his response:
The Type 4A pickup has a larger 1/4" diameter pole piece, and resolves the motion of the larger string (mostly the E), better than the the standard 3/16" diameter Type 1. The magnetic field of the Type 4A is also a little stronger and there is also some ever small effect on the string, retarding it's motion.
Having tried both width poles in the same bass, I found the larger poles to be easier to work with, having more sonic "thickness". IME the narrower poles were more "brittle" and temperamental, though I could get some good deep tones if I worked at it.
Here's a clip of my '51 reissue with traditional narrow poles (Antiquity II pickup)
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And here's the same bass with wider 1/4" poles (Rio Grande "Muy Grande" pickup)
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Obviously not the ideal comparison, since the 2 sampled pickups come from different manufacturers & have different DC resistance, among other potential variances.
I'm still torn over which way to go on my build. I did settle on the wider pickup for my '51 RI but I have a narrow-pole pickup in another bass that totally kicks butt.
