#1
all things being equal, what are the tonal differences? in cleaner amp settings and high-gain settings?
is a high output pickup always better for high gain
#2
I've found that it's the converse - high outputs are better for lower gain amps as they can compensate for it, and lower gain pickups are better for higher gain amps becuase they tend to feedback a bit less.

As far as tonal differences, they're not all identical - most high outputs will break up earlier than others - meaning even on your clean channel, you may get some breakup or distortion.
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#3
High-output pups will produce more gain on their own. You could put a medium output pup through an amp with the same exact settings and the high output will still have more gain in the sound.
#4
high output pups create more distortion with the extra output so generally you can get more gain out of them from a clinical point of view. a good pickup for high gain doesnt necessarily have to have a huge output. high output is nice but getting a good tone is about the pickup having a focused output that can compliment and cut through the distortion to still present the notes accurately without getting lost in the fuzz, so to speak. then again thats all subjective and you might like the sound of a vintage single coil fighting its way through the gain thats set on ten.