Rabbits drink in an entirely different manner than chickens do.
Chicken nipple drinkers have a vertical stem to release the water and conduct it into the chickens mouth when moved out of the at rest position.
The rabbit waterer has a horizontal stem that when moved allows water to run into the rabbits mouth, sometimes via out a small channel where the rabbit can essentially lick it up.
Ever see a chicken lick anything?
Ever see a rabbit peck at anything?
Me either.
This is not to say that these rabbit nipples might suffice in a less demanding situation (few birds per nipple, little competion, lower water needs) but something like a rabbit nipple would never be used in a maximum production situation.
Something we have found in the poultry industry is-
A chicken will spend a great deal of time getting the water it needs to survive but it will only spend so much time beyond that to add to other functions i.e. growth and egg laying. So the rule is make darn sure that they get all that they need to thrive in as short a time span as possible.