yeah there are a lot of principles observed among terrestrial beings . As i can see, the question is more generic and it cannot take us to a valid conclusion. despite this i can suggest these features:

1. the physiology of "prey birds" is different than "birds of prey" like prey birds have long sharp pointed beaks to attack, long separated claws instead of webbed claws, and big wings.

2. the skin color which has a very much impact on a living animal (including aves, reptiles) is designed and camouflaged according to the geographical conditions and soil texture of that particular geography which later on has great impact on food web or food chain.

3. the carnivorous animals have a sharp pointed set of teeth while herbivorous animals have a flat set of teeth.

I am not sure if this is what you look for, but there is some evidence that left and right eye may be used for different purposes in some animals and that the same eye can be used for different purposes too. So any "principles" in animal world have to be inspected carefully not to miss the point.

Diurnal birds of prey often have two foveas in their eyes - used for different purposes. The deep fovea with better acuity is used for far distance observation (side vision) but the shallow fovea is used for observation from shorter distances (frontal vision). Such thing does not seem to be the case in nocturnal birds of prey but they have other adaptations.

Cockeyed squids use one eye to look up to the sea surface while using the other eye to look for a pray in the deep sea, therefore the eye properties and anatomy differ.

Chicken may use one eye to observe the surrounding while using the other one to look for food and it seems to be dependent on the position of the embryo in the egg.

Animals that travel long distances and cannot fall asleep for too long (birds, sea mammals) can sleep with one side of the brain and keep the other one awake. The same happens to their eyes - migrating birds reach high attitudes and then fall asleep on one side, they glide down in a spiral pattern with the outer eye opened and the inner one closed.

As ever, the devil is in the detail. Aspects of eye structure and visual function vary with the context within which they operate. In horses the pupil is a flattened horizontal oval, and the retina is structured to allow monitoring of the visual field along the horizontal meridian (to allow things like wide monitoring of the horizon: see Murphy et al, 2009, International Journal of Zoology, https://doi.org/10.1155/2009/721798); but no fovea as you find in primates.

But even the example you give has caveats. Pigeons have a narrow binocular field in the nasal aspect (or beakward!) in both eyes, and fairly good depth perception, thought to be important for feeding (ie identifying seeds etc and picking them up).

The human vision is particular and I don't think can be compared with other animal race vision. It's a "straight" binocular vision of maximum 220° divided in 4 areas: foveal area, attentive watch area, induced vision area and lateral vision.

As far as you move from the foveal area, the objects perceived will become more grey going slowly to the dark and from distinctive image to totally blurred image.

The attentive watch area, the induced vision area and the lateral vision compose the peripheral vision.

The leading part of the peripheral vision is to detect visual "mass" and to transmit a message to the foveal vision area saying "Hey! Look! There is "something" to see here!".

The leading part of the foveal vision is to catch is "to call" your eyes and your head to turn where the peripheral vision has detected the visual "mass" and to transmit the different "signs" of the perceived image (color, features, shapes, ...) an electric signal through the optic nerve in the to the sensorial memory who will analyze the semiological data and "preselect" the research elements needed by the working memory.

The human eye does not analyze anything, it only transmits the visual information.

Here are 2 links (sorry in French) that explain what I am talking about.

As urban ethologist, I use many times these visual scales in public spaces audits to help architects in terms of use of semiological elements that correspond to the human hierarchy of ocular capture especially in areas like airports, railways stations, commercial malls, etc.

I hope my definition is understandable and not too much scientific.

Wishing you a nice reading.