Re: humbucker mounting
Ring/pickguard mounting: You get a more neutral response form the pickup and considerably less body vibration and it's easier to change its position. Can be a bit wiggly depending on the guitar design.
Hard-mounting: More body vibration into the pickup which CAN enhance tone for some people. More microphonics (squeal) can occur because of the increased vibration. It can be a real pain in the butt to raise or lower the pickup if its not in the right spot.
I hard-mount my pickup, but this was after a lot of trial and error and finding the sweet spot of where this particular pickup should be in relation to the strings. I can "hear the guitar" a bit more, than when I mounted them on the pickguard but the effect is subtle. Likely I won't do this with other guitars unless the guitar is routed specifically for it. Finding the right height, spacers, etc can be a pain. I do like the fact that the pickup is part of the guitar and doesn't wiggle.
The VAST majority of the sound you hear in a pickup is from the metal strings interrupting the magnet field around the pickup, but one of the reasons you hear a sound is due to vibration, either by vibrating the magnetic field or the coils themselves. You DO hear sounds unrelated to the strings through a pickup and there are subtle tones that cannot be reproduced by the pickup unless it's hard-mounted. Whether this is good or bad, is purely subjective. Eddie Van Halen (who not only has/had one of the most sought-after tones but also is an obsessive tone freak) seems to like the results of hard-mounting since every guitar he's made or had custom made has had hard-mounted pickups.... with the exception of the new "Wolfgang Classic" which is really just a modified Les Paul.
