I have observed some of the differences between the behaviour of bats, and that of birds. Where birds sit on branches, bats hang underneath it. A bat can sit on top of a branch, but it doesn't do this because of added balance difficulties. But the real question would be, why birds try their best to sit on top of a branch, while they could just hang underneath it.
As far as i know, a bird would have no disadvantages from this behaviour, and would need less balancing. Thus it would be able to do more, with less energy.
A bat can not fly up side down, neiter can a bird, though a bat can sit on top, or hang under a branch, easily. While a bird will try to keep balance on top.
This would mainly be the case for small birds, obviously. Why is there no species of birds that present this behaviour.. Something to do with digestive system?