Also a late reply, but as someone that has owned, worked with, and rescued parrots of all sizes my whole life, I must say that my friendly chicken breeds are by far the best pets out of all of them. Parrots are like a companion, or a toddler, and are not domesticated the way chickens are. My friendly chickens are very social, cuddly, and not noisy. With a diaper or careful control they can visit me inside too, and will sit happy next to me or in my lap. They don't have the often severe psychological issues that parrots have (parrots being very social and intelligent, have complex psyches). For example, many parrots misunderstand petting as a sexual interaction, especially if you pet them anywhere other than their heads, and it can lead to some severe problematic behaviors, hormone issues, chronic laying (in females, which can be life threatening), and more... whereas with a chicken you can pet all day long and things will be fine.
Also, as an aside, for those that say that pionus are quiet... some may be, but both of mine can out-scream a sun conure easily! Parrots naturally use loud flock-calling (screaming) no matter what the species, though you are correct that budgies flock call is far less intense than their larger cousins.
