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Macaws and cockatoos are both very large birds, some of the macaws include, scarlet macaw, blue and gold macaw, hyacinth macaw, green winged macaw and the smaller hanhs macaw.The cockatoos are no small parrots either, some of the cockatoos include Moluccan cockatoo, Sulphur crested cockatoo, Goffins cockatoo, Umbrella cockatoo.

Since they both are such big birds, there is absolutely no way you will find a cage big enough for both of them. Yes, you do get bird cages big enough for a pair of macaws to live together, but these are not natural bonding birds, they need room away from each other as well and hence will need much larger cages than when you keep two macaws or two cockatoos together.

Second of all cockatoos are heavy when it comes to shedding feathers, dust and dandruff, this does not go well with the macaws.

Macaws need clean air as they do not have the strongest respiratory systems. So the air they breathe should be clean.
Keeping Macaws with cockatiels and african grey parrots would be pushing it as even these smaller birds give out a lot of dust.

Then there is the case of the birds not liking each other, this may result in serious injury as both are capable of bone crunching bites and claws.
So keeping Macaws and Cockatoos in the same house is pushing it, but in the same cage, definitely a NO!

You should also see the noise factor which be like Infinite! LOL.