I'm the unusual one at the opposite end of the spectrum- I play 11s and 12s at standard tuning, with medium to high actions and extra heavy picks.
The reason? I read a Steve Howe article when I was a kid that he glued credit cards together to get the thickest possible pick for dynamics- He could always loosen his grip for light parts and tighten up for power.
The pick thing worked and as I increased the difficulty across the board, I noticed a number of things
1. I did have substantially better dynamic control than my buddies
2. I was much stronger
3. I could play far more intricate parts (especially complex rhythms) because the strings didn't flop around- this includes faster arpeggios as long as long as open strings aren't included
4. And recently, I've realized that much of the strength of my tone comes from heavy strings, the ability to hit them hard for growl and back off for the cleaner parts (taking a repeating arpeggio from clean to growl based on string pressure is a perfect example).
Negatives are pretty obvious-
1. I always require locking tuners
2. Pull offs are a little easier with a lighter action, but intricate tapping or sweeping a mix of open and fretted isn't as easy in heavy land.
3. Left hand only notes are actually easier for me, but reaching over to tap with the right hand is difficult.
It's funny, I have one light string low/action guitar that we use to demo pups and it's set up with 9s so practically anyone can play it. Tonewise, I can only get 90% of my sound with light strings, however, it's easier to play simple, straight non-complex rhythms and I end up tapping and sweeping all over it on auto pilot- kind of case in point of the stuff I give up for my sound.
Hope this might be helpful to someone else- there aren't that many of us