Nestling passerines (specifically swallows, bluebirds, and sparrows, though I’d guess most are the same) have rubbery-feeling skin and very soft downy fluff, and prickly little claws. They feel very delicate.
Starlings have sharp claws (at least the captive ones I’ve worked with, they may wear their claws down more in the wild).
I’ve had pigeons land on me a lot but they generally won’t let me pet them. They also bite!
These big moths are fuzzy and their feet feel sort of adhesive on your skin, as do the feet of butterflies. I like picking up big lepidopterans that are torpid on chilly days, and watching them warm up from my body heat. Sometimes when they’re warming up, you can feel a bit of vibration as they shiver and buzz their wings.