I have 2 EE's and one Ameraucana. The Ameraucana was bought as a 2 yo hen and is not docile because she came from a breeder (lots of chickens, was not handled).
My 2 EE's are not as skittish but not my friendliest either.
Hands down, my most friendly chickens are the Salmon Faverolles though none of them are mean and I can pick up all of them except the new girl.
My advice: if you want a guarantee that you will get a colored egg, it's the Ameraucana only. The EE's carry the blue-egg gene but they are NOT a standard breed and can lay any color, there is NO guarantee you will get a blue or green egg from an EE.
If you get the Ameraucana (which is a recognized breed) get it from an actual breeder. If you buy from an online hatchery or the farm store, it is an EE, despite what the sign says.
To increase your chances that the bird will be friendly, get them as little fluffy chicks and handle them!