This depends entirely on your own personal preference and what plans you have for your bird or birds.
I’ve recently sold some baby budgies and have been asked this question a few times and have always responded with the same answer.
If you want a companion bird, ie. one you can handle, tame and possibly train then go for a cage. If on the other hand you would like your bird to live out as natural existence as possible then go for an aviary. This is the basic jist of it but of course it does depend on your budget and the space you have available.
The majority of my birds live in a large outdoor mixed aviary at the bottom of the garden, but when I have babies to deal with I put them in a cage once they have flown the nest to try to keep them as tame as possible ready for sale. This also makes them much easier to catch once new homes have been found for them.
A caged bird will become much tamer and more human-friendly because it will undoubtedly interact with people more often. Whereas a bird in an aviary will live in a semi-wild state and will only be used to its main owner.
I do believe however that if an adult bird is taken from an aviary to be re-homed in a cage then this can have a psychological effect on it; after living semi-free in the aviary for so long this would be like a prison sentence to the poor bird.
On the other hand if a baby bird is first housed in a cage and has never known the relative freedom of an aviary then it will accept its existence as normal. This will not then affect the bird psychologically in any way. If the previously caged bird is then given the freedom of an aviary then initially it will wonder what’s gone off and will tend to stay put to start with. After a day or so however it will then begin to explore its new environment and will soon get used to the change.
Unfortunately this wouldn’t work the other way and a previously free bird that is now caged will undoubtedly become depressed.
To summarise moving an adult caged bird to an aviary will generally be fine, but moving an adult aviary bird to cage is not a good idea.
The only exception to this rule is if the bird becomes ill it will and should have the solitude of a cage whilst it recovers from its illness, this also quarantines the bird so that if the illness is infectious then the risk of the other birds catching it will be dramatically reduced.