There is more in common with faeries and bigfoot than most of your proponents will try to avoid.
Both have historical accounts and stories from indegenous peoples and preindustrial societies. We are told the native american accounts of bigfoot like creatures are significant.
Lots of bigfoot behavior I've read is fairly similar to faerie stories. The zapping,infrasound, confusion, gifting, psychic powers, stick structures, wood knocks, rock throws and general mischief making. They could all be faeries or bigfoot.
All the faerie encounters people report to friends or law enforcement must be considered as well. How could people from 1000 years ago to today give consistent accounts of faeries and there be nothing to it? Are they all on drugs, hallucinating, hoaxing, lying, mistaken, insane?
There is some evidence for faeries people collect in the form of faerie dust, pictures, footprints, etc. like the bigfoot evidence we have the authenticity is suspect. No faerie pgf though that i know of.
The big difference now is we know better. We have science and know there is no real magic or faeries they dont really fit in with the modern worldview. Bigfoot, aliens and ufos, can fit snugly in the cracks though. Bigfoot fits in with what we know about evolution, migration patterns, etc. So are obviously fake but bigfoot is plausible.
The biggest similarity though is we have no conclusive evidence for either