I really don't recall the Hawk Headed Parrots personality attributes, but I can definitely help with the amazon.
If you are prepared to buy an extremely large cage, possibly two, (try www.bird.com or www.featherfarm.com) and to consistently buy your birds toys. Give them a specific diet of fresh fruits, vegetables, pellets, and even certain seed mixes as treats. If you can give them at least one hour of time out of their cage every day with human interaction and don't mind taking a few bites from a frightened bird, then yes, you can probably handle it.
These birds are known for going through toys very quickly. It also depends on your birds individual personality, as well. Some of my parrots shred wood like it's paper, and others would prefer to only nibble.
It honestly is a life style change to take care of these parrots, they are like children. They need supervision, play time, and a lot of love and patience.
Get your birds after they are done being hand fed from an accredited breeder. If you can get them near you, have the breeder teach you how to hand feed yourself so you can do it for the last couple weeks. This is a great boding between the owner and the bird.
As for the noise level, expect it during the morning and afternoon when you come home from work. The amazon is probably going to yell words more than anything if it's anything like ours. I don't think the lilac crowned is as loud as some of the other breeds like the double yellow headed, yellow naped, ect.
Good luck :]