We have a male (Henry) and female (Angel) Eclectus and both have different personalities. Henry can be jealous of Angel and will play up a lot more when they are both out together. Henry will go down to the floor and happily wander around checking things out. He will fly to the shoulder of my partner or myself and nibble on our ears. Henry is out-going within our family to a point. If someone comes around and is here for more than 10 minutes, Henry will start to talk to them. Usually "hello" and "what are you doing?"
Angel will only be lay back when on the play gym and will happily sit and preen herself. She will lunge at people when in her cage Yet will take a sunflower seed. If she get onto the floor she goes into breeding / nesting mode and will chase off anyone, expect for me (she loves me).
I find that Henry is more approachable, Loud, curious, persistent, observant, jealous and head-strong. But he is also affectionate and gentle. This is because Henry has been with us from 10 weeks old.
Angel is more aloof, quiet, aggressive and when nervous or scared she will swear a lot. This was because of her previous owners. After many bites and blood she will only allow me to handle her and is now quite affectionate and gentle with me. Angel is slowly becoming more tolerant of the family.
I believe that the home environment has a huge impact on the personally of a pet. Henry has had more social interaction than Angel, who had very little social interaction. This is shown in the personally and behaviour of each bird.