I would guess part of this relates to ancillary equipment. Pedals weren't that big a deal when minis were first out. But now more guys want a clearer 'more of my guitar' type sound, with a pedal board full of dirt, whereas full hums are more about 'pounding the amp into submission', in a rock context. Lower output hums are very popular now - isn't that what a mini is, boiled down to essence?
Just musing aloud. Could be wrong. But I had a guitar with minihums for a while and LOVED them, the guitar itself not so much. Would buy again.
No, a mini humbucker isn't necessarily lower output. Look at a Seymour Duncan hot rails, it's a humbucker the size of a strat pickup and it can keep up with any full size humbucker. Maybe the theoretical highest output of a full size humbucker is higher, but no one is designing pickups to that limit.
The length of the string that each pickup senses is different. A full size humbucker covers a greater length of the string than the wavelength of higher harmonics, so you'd get some cancellation and loss of high-end detail. There's other differences too, like needing to use thinner wire to fit as many winds in a smaller pickup, which affects the impedance and thus the way the circuit reacts to whatever you're plugging into.
This kind of shootout is a little pointless because there's a range of pickup styles for each. But if he's showing "here's what I consider a typical sound for each of these types of pickups" then that could be useful.
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