In my opinion, depends on the bird and how well a person knows it. Dominance is a load of crock, so that is a non-issue.
To me, it boils down to how much of a brat the bird is going to be while it's there. Is it a bird who is known to bite faces, necks? Moody and easily upset? A bird that redirects it's aggression, or one that will ignore a command/request to step up if it doesn't want to and knows it's somewhere awkward? Does your loving, cuddly, and extremely hormonal bird have a fetish for your head?
Probably not a good bird to let on your shoulder, large or small. (Just, with the small ones we pay less for our mistake. People could loose an eye to larger birds, little beaks mean less damage.) Some people will not allow their large birds on their shoulders at all, no matter how sweet, just because their capacity to do damage if they ever were to bite when upset.
Peanut, in nearly 14 years, has bitten me on the face and neck once each, both when she was young and at her most bitey. She does not bite when I try to remove her (though sometimes she will try to dive into my shirt if she thinks it's bedtime and I want to put her in her cage.)
So, because her good behavior I trust her on my shoulder. However she prefers clinging to my chest or being carried for some reason when I move around with her. When sitting, being in front of me, in my lap, or on my chest means more cuddles for her. Sometimes when she's feeling sleepy she'll huddle right by my neck, behind my hair a bit, and sleep. (It's a pain in the neck, I feel like I have to lean away a bit or I'll squish her, so she moves even closer.
)