They CAN be loud, I can attest to that. But I don't think they are as 'noisy' as cockatiels. In my experience, their loudness has several pitches. There is the 'piercing' sound that goes right to your ear (and loud enough it can make your ears ring)
I don't think there is a such thing as a quiet bird. But the sound and volume levels do range. Budgies have the sweetest tweet, but it's also rather low.
My Skittles was very noisy at one point. IMO, and its just that, MY opinion, the degree of 'noisiness' of a parrot depends mostly on the environment it's in and the level of attention it gets. Ignored birds WILL be noisy.
Skittles used to go on and on and on during the day. So I arranged my life to accommodate his needs. Not everyone can do that. For example, when I do my dishes I let him sit on the faucet and watch (actually he lets himself) etc.
They just like being with their owners. I find they are rather quiet when they are out of their cage and with the owner. The only time Skittles goes off is if I leave the room and he can't follow me (if hes in his cage for example) if I leave the apartment, am on the phone or someone unknown comes in.
Unfortunately, I have to cage him if someone comes over cause he will attack them. I'll be the first to admit he is not properly socialized - but the way my lifestyle is - its nearly impossible to do that anyways.
Now, I'm gonna go out on a limb and make a few suggestions that may people may OR may not agree with, that's okay. It's just my opinion.
When he/she acts up -give a verbal command to stop. If they persist, cage them and cover them up. If they persist, put them in a dark room.
What I had to do to Skittles is buy a 'time-out' cage and when he was naughty and didn't respond to verbal commands, I'd put him in the timeout cage and put him in the bathroom, in the dark, and close the door. 10 minutes later, I'd go back and check on him. If he was behaving I'd take him out - if he continued a short while later, I'd repeat the timeout. I did this for about six months. I dont even have the timeout cage anymore cause I dont need it. He is that well behaved.
NEVER hit a bird or even its cage. You can raise your voice, but don't 'scream' at it.
Now, Skittles LOVES water and loves to bathe. But he always HATED being 'sprayed'. So I built on that. I have a water bottle handy AND get this - if he is behaving and I pick it up, he does nothing. IF he is misbehaving and I go for the bottle he takes off cause he knows whats coming.
This has not damaged our bond in any way. He will lay beside me on his back and even let me hold his wing and spread it out. I can even clip his toenails. If he was holding any grudge or having a trust issue I wouldn't be able to do so.
Now for those who may think its cruel to do the timeout, let me just say this - I've seen people do worse to their kids. My own neighbor trained her cat with a spray bottle, thats where I got the idea.
His own breeder told me not to do these things. Even the vet suggested not to do the water bottle. BUT everything they suggested DID NOT work. But what I did worked. Not that it would work for everyone.
Now, a final tip on biting. You cannot teach a bird not to bite. It's not in their nature - and birds biting is really their only defense aside from their wings. They use their beaks to explore and test things aside from biting and chewing. I managed to get Skittles to stop 'biting' me hard and breaking skin. Now he just nibble-bites. What I did was when he was biting me, I'd grab his beak and hold it between my fingers and say 'no biting'. It works.
I got very frustrated back then and got a lot of flack from 'professionals' whose advice didn't work. I'm sure you all have been in situations like this - if not with your birds, with your other pets or other family.
Just please know, I mean well!
I don't know why I posted all of this - actually, I do - but I'm not gonna tell ya! LOL