In English, bird brain is a pejorative. The top Google search result yields a definition of ‘an annoyingly stupid and shallow person.’ Nonetheless, bird brains and human brains have many similarities. They have structurally divided, bi-hemispheric brains and lateralisation of functions, just like us and most other vertebrates, but how they differ is more interesting.
I’ve extracted the majority of information on this page from Iain McGilchrist’s publication The Master and His Emissary with a focus on birds.
Firstly, except for birds of prey—because they have forward-facing eyes—, birds don’t have stereoscopic vision. If you’ve ever noticed a pigeon or a chicken strutting about, they jerk their heads around. This is to render a better perspective of their immediate surroundings.
Recall that the left hemisphere is about contraction and closure. The right hemisphere is open and expansive.
For birds, there is a need to focus attention narrowly and with precision, for example, on a grain of corn. At the same time, there is a need for open attention to guard against a possible predator. But apart from the optical mechanisms involved, there is the cognitive need to focus attention, but it is an impossibility to focus on both simultaneously. There is a trade-off between close focus and wide focus. To do both is to do both poorly. The trade-off is to eat or be eaten, so this is a nontrivial conundrum.

You can simulate this yourself. Out of doors or in a large-enough indoor space, hold a page at arms’ length and try to read the words on the page and keep the background in focus.
Returning to the birds and remembering that, like us, the left eye is controlled by the right hemisphere and the right eye is controlled by the left. You should suss out by now that this translates into the right eye for getting and feeding and the left eye for environmental vigilance.
Although they are better at detecting predators with the left eye, many types of birds show more alarm behaviour when viewing them with this eye. If they detect a predator with their right eye, they will also choose to re-examine it with their left eye to the extent that they will turn their head to make the visual connexion.
Like humans, chicks preferentially use the left eye (right hemisphere) for gathering social information.
Like humans, chicks preferentially use the left eye (right hemisphere) for gathering social information. They use this eye to differentiate familiar members of the species from one another and from those who are not familiar. Some species seem to operate opposite to this, but they are the exception.
One interesting bird of note is the wry-billed plover of New Zealand. With a beak that curves to the right, it favours the left hemisphere for focusing on feeding.

McGilchrist notes that “there is a strong right eye (left hemisphere) bias for tool manufacture in crows, even where using the right eye makes the task more difficult”.
Another feature in common between humans and birds is speech vocalisation as it were. In both cases, speech articulation is the domain of the left hemisphere.
“The right hemisphere in birds, as in humans, is associated with detailed discrimination and with topography; while the left hemisphere of many vertebrate animals, again as in humans, is specialised in categorisation of stimuli and fine control of motor response.”
The right hemisphere yields broad, vigilant attention, and it is involved in bonding in social animals.
In general terms, the left hemisphere yields narrow, focused attention, mainly for the purpose of getting and feeding. The right hemisphere yields broad, vigilant attention, and it is involved in bonding in social animals.
“The right hemisphere underwrites breadth and flexibility of attention, where the left hemisphere brings to bear focussed attention. This has the related consequence that the right hemisphere sees things whole, and in their context, where the left hemisphere sees things abstracted from context, and broken into parts, from which it then reconstructs a ‘whole’: something very different.”
