From my limited experience, a parent raised bird that has learned to trust humans will keep their trust when "ignored" for several months over a hand raised bird that became "untamed".
However, this can vary depending on how the bird was trained. The majority of my birds are second hand, plus. I only have one that never had a previous home. That's Casey! She was 100% human raised, and it shows! Casey will be turning 16 this year and she's been with me since she was 5 months old. She's never lost her "tameness".
Then there is Pistachio. I know he's older than 19 years old, but I don't know by how many years. He came to me as a very skittish ex-breeder. Although my goal was to never tame him, I did earn his trust in an accidental experiment. (his daughters fault!) All I did was feed everyone by hand first thing in the morning before providing fresh foods. Although he still has some skittish like behavior, he has no problem flying directly to my hand to eat from me. If Casey isn't the first to my hands, he is! Even if it's been several months since I last fed them by hand! When I refresh the food dishes, he may fly off initially, but then once the food is back, he flies back, regardless if I'm next to the dish or not. He's no longer a terrified bird.
Tomi Girl, age unknown female cockatiel. (assumed teens or older) I think she might have been hand raised but I honestly have no clue. The last people who had her found her in their yard, then nearly killed her... I'm guessing that she was hand raised because she doesn't act like a parent raised bird. However, she also doesn't seek out human interaction. She's kind of quirky! If I don't keep up on hand feeding her by hand (seeds, pellets or treats), she "reverts". Reverts as in, it takes time for her to rebuild her confidence and trust in eating from my hands. Saying that, I always have to be careful with her! Whenever I'm doing anything inside the cage that requires having the cage door open, her *favorite* spot to sit is on the perch attached to the door! And of course she sits on the spot closest to the side that the door opens away from. If I open the cage, I have to make sure not to hit her head against the side of the cage, or when I go to close it, I have to be careful not to smash her head between the door and the side! I don't know why it's her favorite spot, but she enjoys sitting there even with the door wide open! (she lives in a 5 x 5 x 6 walk in aviary...)
And then there is Faye. Age unknown female cockatiel. (assumed teens or older) Like Tomi Girl (and Pistachio), she's had a bad past and multiple owners. I have no doubt that she was hand raised and well loved some point in her life, even if it was just her breeder! I knew that shortly after getting her, she was no ordinary cockatiel. She took after Pistachio's daughter, in wanting to eat from my hands, even went as far as demanding it, despite the fact that there was food already out for her to eat! She's never shown any desire to have any more physical interaction beyond being fed by hand, so I left it at that. She demanded to be fed by hand for a long while, but I stopped feeding the flock by hand, so she became like Tomi Girl. Leary and unsure of being fed by hand. Recently, she became sick and I had to separate her from the flock. During this time, she has accepted getting head scritches, and sometimes I can't get her to step up because she wants her scritches! She wanted out of the cage so she could hang out with humans. (even managed to escape once!) She gets upset when humans are eating non-bird safe food! (comical to have a bird standing on your pizza plate, stretched out as far as she can, trying to get a bite of that pizza!) Faye had to get medication for an entire month! And instead of cowering away or losing trust in humans, she's seeking it!
If a bird is raised and trained right from the start, I doubt it matters if the bird was parent raised or hand raised! Like Mizzely, I'd be okay with a parent raised bird! Casey is the youngest, hand raised bird I've had, so I never really dealt with a baby bird growing up and getting nippy with all the hormones and gunk to go with it!
I can interact with baby hand raised parrots no problem! But I think I'd still enjoy the kind of relationship that could be had with a young, parent raised bird.
Saying that, I do have Sylphie and I'm torn on what to do with her. From the information that has been given to me, she is most likely a wild caught parrot imported May of 2013. Can't get any more parent raised than that! Age? Who knows! No way to tell if she was a young, wild caught bird or an adult, wild caught bird. I'd personally love to see her in an aviary with others of her species, but aviaries around here are few and far between. An aviary of her specific species? None. I'd probably have to transport her 3 or more hours away to find the kind of aviary I'd want her to live in. I'd rather see her living in a flock situation rather than being a pet, unless I could find someone like
@InTheAir to take her in. In other words, I'm not willing to let her go to just anyone! They'd have to be very special!
I could train her myself, but I don't need every one of my birds to be tame and friendly, as long as they are happy and content. If they seek out more physical attention, then I'm happy to oblige. I did actually start working with her, and we've figured out a way for me to refresh the dishes in the cage to cause minimal amounts of stress, but after finding out that she's wild caught, it pains me to see her in captivity. It also explains her abnormal behavior that isn't typical of parent raised birds raised within captivity!
I personally never want a baby again (puberty hormones in a parrot are no joke LOL) but if I did, I would prefer a bird that was CO-parented - where the mom and dad bird do most of the feeding but the breeder also gives some feeding too. Or, I would probably choose parent fed with just human interaction. Why? Because I want a bird that knows its a bird. Birds who think they are humans have a lot more behavior problems in my experience. 
