Well, in a nutshell, nothing does well when too restricted and in an overly hygienic or overly unhygienic environment, barring of course individuals with immune diseases etc or those with amazingly tough immune systems. Even cage bred pet birds like budgies etc exhibit self/other destructive traits and anxiety if their cages are too boring, so how well you birds do will depend in part on them and in larger part on you and how you set up their cage.
Keeping animals on the same ground for the long term also leads to greatly increased risk of almost all parasite and disease threats, so having two separate cages is best, which will aid in health care and also enable them some variety and stimulation. Neuroses and negative behavior traits will emerge if they're kept in under-stimulating conditions. Chickens aren't as stupid as many people think, and they need some level of stimulation to truly thrive. For the most bare cage setup, hybrid layers or meat birds would probably do best since they're often bred under such conditions and are correspondingly dull of mind, for the most part. Many Silkies and other bantams are also bred under very restrictive conditions by some breeders and can cope as well, but I assume you're after eggs (?). All breeds have some strains kept under very restricted and non-stimulating conditions and they can cope well under such conditions, since it's all they've known and they've been bred for it, but free-range bred birds can basically lose their minds if suddenly restricted to such a barebones existence.
Whatever cage setup you use, basically any breed would be ok within it, as long as it's set up to give them enough quality of life and provision for health, i.e. room to exercise and some sunlight, some shelter, etc. Even goldfish don't do the best when they're able to see all the walls of their existence without moving from the spot. In zoos they found that L-shaped cages vastly improved animal's depression and destructive behaviors because there was a corner to check around, an area they couldn't see from all other corners, something to wonder about and explore.
Even if you have the world's greatest cage you're going to need a quarantine cage as well. It may be small yet still do its job, but in the event of some serious outbreak of something that is nigh impossible to get rid of, you will do better if you have two equal sized cages, in case some or all of your flock or another new batch of animals seem to have to permanently live separately for whatever reason. There's always some emergency sooner or later that puts many unprepared animal owners in a bad situation because they didn't have a spare cage available. Injury, illness, intolerance, etc are likely to happen sooner or later. Having only one cage will bite you sooner or later.
Sorry for the off-topic aspects of my response, I don't know what sort of setup you have or intend to have so I'm trying to cover a few bases. Best wishes.