The ability to sleep whenever and wherever they want.
Heck, just the ability to sleep!
No, I don't want to turn this into another of my "I haven't slept all day" rants.
Somehow, a mosquito hawk got in the house... you know, those insects that look a cross between a daddy-long-legs and a mosquito? Too many people actually mistake them for mosquitos, but they're way too big to be. In fact, they prey on mosquitos; rip them up, tear them up, and eat them up (okay, stop singing, Aryx).
Well, two pairs of eyes discovered the mosquito hawk at the same time, and followed it about the room. The owner of the younger set of eyes started chittering. Cats are weird.
The hunter became the hunted.
They lost interest in the skeeter-eater after it flew out of the room.