I found this answer of Jenny very informative.
I have 3 eclectus parrots (and also breed my pair) and one african grey. We've had the african grey for over 10 years.
Having both types of birds for many many years, knowing A LOT of others that keep both types of birds, here's what I have to say on the matter.
African greys are generally one person birds. They pick one person in the house that they like and just tolerate anyone else. Our grey picked my husband even though I'm the one that takes care of him. He likes me well enough to allow me to feed him, clean his cage and pick him up. He won't allow me to cuddle with him, scratch his head and he will not let me play games with him..he gets grouchy at me. LOL He talks quite a bit...but on the downside of that for the first 5 years we had him, at 5:30-6 am every morning he started yelling for everyone in the house to get up. Not only that but for several years, if we didn't put his cage in a spot that he could see you when you walked out of the room..he'd sit and scream bloody murder until you came back..where as our eclectus will just come and find you. LOL
Greys are very smart and because of that can be a bit high strung if not kept constently entertained, as in all parrots, but more so in these guys.
Our eclectus...we have 2 females and a male. Our one female is about 7 years old and our male is 6..the other female we have is a baby of theirs we kept from a clutch a couple of years ago. They are actually quiet in comparison to most parrots and that's initially what attracts many people to them.
The female eclectus have a reputation for being temperamental after they hit maturity...but that, like all birds is part of growing up. You have to work through those stages and realize that birds are highly intelligent, sometimes finicky creatures and sometimes you get bit. They aren't like dogs that trust anyone that hands them a piece of food. You have to learn to read their moods, when they want handled and when it's a good time to leave them alone. The ONLY time I've seen an extremely overly aggressive eclectus parrot is one in a mating situation. I recommend to everyone that buys ekkies from me, if you want them to remain a perfect pet, don't pair them up. (but again...that's with most types of parrots) The females RARELY remain pet quality and the males get temperamental during mating and egg laying...although the rest of the time they revert right back to being good pets.
Male eclectus are a completely different creature all together. They are loving, affectionate, playful and outgoing. It doesn't matter who walks in our house, our male wants to know who they are. He'll fly and land and ANYONE. He likea attention from anyone...me, to my husband..our two boys and even a friend that comes over that he's never seen.
Although, he's mama's baby boy and everyone, including him, knows it. LOL
They also are EXCELLENT talkers. They can make male and female sounds..the higher voices and the lower. Our male ekkie actually talks MORE than our african grey, and it's just as clear sounding.
To anyone that says eclectus don't talk as well as african greys, I'm here to say..you are sorely mistaken. A perfect example of that is Riley the male eclectus published on youtube.
Should I buy an African Grey or Eclectus Parrot? - Yahoo! Answers