Fair enough, but that's more than one parameter changed.
Not sure if I was being ambiguous or misunderstanding the terms of art when I said 'taller'... How would two pickups built with the two bobbins below differ in output or sound quality, if at all, given the same wire, same number of winds, same aperture, if the only difference was one was taller? The substantive changes was the taller one would have more wire closer to the core (but more wire would also would be farther from the string*), and the core itself would be taller (more ferrous and/or magnet mass, depending on whether the magnet is in the core or under it).
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Okay, this gets closer to what I was wondering. How would the sound differ if your coils and magnets were 3/4" tall or 1.25" tall, but the number of wraps and bobbin dimensions were in other regards the same?
*(EDIT: Bruce answers this part of the question in post #435. Thanks!)
I think my answer still applies. Basically, think Telecaster bridge pickup vs Jazzmaster Bridge pickup. The taller pickup would be more focused and brighter and the wider pickup would be fatter or "fuzzier" as Mr. Bruce put it.
The more magnet or steel to fit the taller coil, then you're going to be increasing the inductance of the pickup. If it's just a magnet, you're using a bigger magnet, so it will be louder and brighter. If you had the same sized magnets underneath with a steel core, adding more steel may cause you to lose a little bit of top end. That loss may or may not be perceptible. The output level would be about the same.
The best way to find out is to wind two coils like you described yourself. I can give you my own speculation, but it's not really meaningful until you actually perform these experiments and hear the results for yourself.
Sound "quality" is a really subjective topic. That's more of an issue of personal taste, really.