I wonder if bird brains are also more energy efficient as a result of the greater neuronal densities (since that implies shorter wires).

Yes - that seems to be the point of that poster I found earlier.

From an evolutionary point of view it makes sense - birds are under tremendous optimization pressure for mass efficiency. Hummingbirds are a great example of how far evolution can push flight and weight efficiency.

Primate/human brains also appear to have more density optimization than say elephants or cetaceans, but it is interesting that birds are even so much more density efficient. Presumably there are some other tradeoffs - perhaps the bird brain design is too hot to scale up to large sizes, and uses too much resources, etc.

Unfortunately I can't find the full paper of the abstract you linked to to check the details.

It was a recent poster - so perhaps it is still a paper in progress? They claim to have ran the defractionator experiments on bird brains, so they should have estimates of the actual neuron counts to back up their general claims, but they didn't provide those in the abstract. Perhaps the data exists somewhere as an image from the actual presentation. Oh well.