I am a collector, and I know, there are a lot of us out there. To improve our lives, I have the following two small suggestions:
1) Add an NBT-data tag to the bird cages and butterfly jars, containing the name (would be best), the colour (next to best) or at least a number of the caught animal. Display this tag in the tooltips. That way, the caught birds/butterflies would be easier to recognize, especially when sitting in the inventory. It would be much easier to check, what you've got and what you are still missing.
2) Add an easy way to transferbirds form one cage to another: At the moment, you have to release them and try to re-capture them again. I suggest, just right-clicking with an empty cage on a full one, placed in the world, would tranfer the bird. This is useful only for birds, as there are 5 differnt types of bird cages, but only one type of butterfly jars.
I think that it is a good idea but another thing could be bigger bird cages, they are connecting like gates aand pillars and fences and when you right click it with a bird cage with a bird then it will transport. or maybe it could just be placing down multiple cageswill connect, this would be useful for displaying more birds and it could be similar to a fish tank. (They should add fish tanks after they add more sea life)