Thats a tough one! I don't have experience with greys or macaws. I have a lot of experience with Aussie cockatoos. I think it depends on...
1. what you personally want from a bird; what traits in a companion parrot are most important to you. The little stuff isn't as important as the things that you really hold dear.
Cockatoos are generally cuddly, bossy, loud, dusty, mind blowingly heart melting adorable, they arent great talkers usually (except for some corella species), most aren't pretty, snuggly, puppy like, very intelligent, untrustworthy, chewers, clowns, an entertaining blast to own.
Greys are normally sweet, talkative, impressively intelligent, easy to get along with, trust worthy and lovely companion. (grey owners could elaborate)
Macaws seem talkative, destructive, more trustworthy than a cockatoo, beautiful, sweet and sassy, very clever, somewhat clown like (macaw owners could elaborate)
2. what YOU can offer a highly intelligent bird; how much time do you have and what kind of activities can you split your time between? Are you the kind of person that has slow, calm, gentle movements or are you a more energetic, bubbly and bouncy person?
Cockatoos love colourful personalities

If you love dancing around like a loon, your cockatoo will happily dance around with you. Cockatoos are like a little feathered puppy-dog-child. They also love calm gentle people and if you learn everything you can about their behaviour and mix up their activities, they are very adaptable creatures... stuck in a routine however they can become very stuck in their ways and act out accordingly (don't let your cockatoo get stuck in a routine

OR think he is boss ).
I know greys can learn to tolerate and live with a lot if conditioned from an early age, but from what I have learnt they seem to prefer a calmer environment and most prefer talking and head scratches to dancing around, cuddles and playing like cockatoos do. I have heard they can be very fussy naturally and will initially treat all new situations, people, objects etc with suspicion. They are more emotionally deep and intelligent than a cockatoo and are more like a calm child. I get the feeling they would be the ultimate companion for a single person who rarely has another person to talk to.
I think Macaws are a bit of a mix of the two, a gentle giant who can be silly and loves playing but is much calmer/more relaxed than a cockatoo. I know next to nothing about macaws

But I get the feeling if you smooshed the personality of a cockatoo and a grey into a huge brightly coloured body you would get a macaw.
3. what can you tolerate; what kinds of sounds make your blood boil (volume is sometimes less important than the type of sound), are you the type of person that is able to sit still for half an hour or longer while your cockatoo requires snuggles etc.
Cockatoos calls vary between species, some (like the galah) have a very high pitched ear piercing scream that as far as volume goes is probably not even as loud as a sun conure. I would even say its possible to keep a galah in an apartment if its well entertained. But the high pitched nature of the call can be highly irritating to some. Bare eyed cockatoos have a really amusing quavering call that is VERY high in volume (probably even louder than a greater sulfur crested) but its rather amusing... sounds a bit like an opera singer. Mine only annoys me because I know the neighbours could hear him, otherwise I wouldn't care at all. He looks ridiculous calling as well, he opens his mouth stupidly wide LOL Most other cockatoos have a very harsh scream, some have a mournful whine. Try youtube to get an idea of which sounds you can tolerate.
Greys make a variety of sounds and are so good at mimicing... there is the potential for them to pick up sounds you hate and repeat them to their hearts desire... the phone, a fire siren, your alarm clock, a phrase you get sick of hearing LOL Some love to talk and make sounds all day long. If you can't stand people talking at you all day long, think long and hard before getting a grey
Again to me the macaws seem like middle ground. They seem to me like better mimics than cockatoos but arent as chatty as greys. They also seem to have a comparable call to a cockatoo, but louder or smoother? Again, I know next to nothing about macaws but have seen a few youtube vids
