Bill Lawrence has claimed all along that the type of magnet makes no difference, its the way its used and the amount of magnetism it has. To me, that makes some sense, but it might not to others. Most folks, I think, would say, well of course, and an AlNiCo V is more powerful than AlNiCo II so therefore the type of magnet does matter. To a certain degree thats true, but only if the magnets are charged to full capacity. They may, or may not be. Here's the thing - the designer, boutique artist, factory... whatever... will balance the magnetism, the space the magnet can occupy in order to make its magnetic circuit, along with the coil shape, wire gauge, insulation thickness, bobbin/magnet/coil spacings etc... to make something they feel can sell. When you change the size of the magnet, you change its circuit. That will alter tone. So its entirely possible that you want to keep the magnet a certain size, and and change its relative force. Also tradition and pre-existing designs may dictate what is acceptable for the magnet size - also requiring different charges on the same, or different magnet types. Its all a witches brew. You cant say this, vs that with absolute certainty.
Higher DC coil ohms will result in high frequency fall off.
Heavier wire will result in lower DC ohms, and give more highs, but less overall output.
Stronger magnets tend to offer higher output
Low wide coils are offer several reasons to give more mid tones and heavy low end, over skinny tall coils (P90 vs Strat shapes)
Stronger magnets are usually used with lower DC ohm coils to maintain output strength and offer brighter tone by having less high fall off
And so on and so forth... until your brain explodes from overload.