I can't speak for a parrotlet, I have a ysgcc. She is not much of a "snuggler", but we're still bonding. She does love to leave her cage & have direct contact with me. She is quite nippy & strong minded. I guess she's like her mama.
I have no idea about the conure, but I have a male parrotlet and I can tell you about him. Goofy is very independent. When he wants to cuddle and have his head rubbed, he's a very sweet little being ... the second he's had enough, that's it! Better be watching his body language, or your fingers will hurt LOL He has days when he likes to ride on my shoulder, and other days when he'd rather just play with his toys and have minimal interaction. He LOVES the shower, loves the house to be as loud and chaotic as possible (when my dogs play in the room, he gets really happy and excited). He is tiny, but completely unaware of his size. Think of a parrotlet as an amazon parrot in a teeny tiny body. He can be moody, loving, and often independent. He is not needy at all, and is very content to play with his toys by himself as long as there's some sort of commotion with people and pets in the room to entertain him. He is not terribly loud, but he does steadily chirp to himself as he plays during the day; and if I go outside, when I come back he will squawk to let me know he didn't appreciate being left alone.