Easter Eggers can vary so much, being of mixed genetics. Ameraucanas, on the other hand, I've found to be super sweet birds, at least the ones have out of the Cree Farms line. I've had blue, black and splash, still have one black and one splash, 7 years old, and golly, we'll miss those hens when they're gone. They're even laying now! Great hens.
My EE hen who is 1/2 true Ameraucana is friendlier than my hen who was a project for a new Ameraucana color, but they are both good girls. And the one I made by breeding my late BR rooster over one of the blue Ameraucanas is a doll (when she isn't in a molt-then, she's a crazed lunatic, flies into walls to keep from being touched)
Generally, food is the way to a bird's heart. Sit quietly with food in hand and let them come to you and don't try to grab at them. Eventually, most learn to trust and you'll be able to pick them up.