Evolution adapted the eyes of different species to different types of environments. There are Nocturnal, Diurnal and arrhythmic types and each section has their predators and prey animals. First we take a look at the size of the Lens of the different species.
Nocturnal animals have big lenses and a small Vitreous Humor. Their eyes work as a sensor for movement in the dark and mainly use Rod type cells for night vision. The big lens also converges more light and gives a brighter image.
Diurnal animals have small lenses and a big Vitreous Humor. The small lens gives more depth of focus and focus becomes less critical. For human, the lens also clearly projects what’s right in front of the view-line on to the Cone-type cells of the Retina, sensing color information and high acuity.
Arrhythmic animals have medium lenses and a medium Vitreous Humor. This gives a mix of the above type of animals providing them the ability to live during the day or to roam during the night.
Second are the pupils, they work as the Primary-Alpha-Areas of the eyes, and contract when light is increased or when more focus is needed, in contrast to Alpha-Areas that surround the eyes although the eyebrows can be frowned and eyelids can be narrowed to increase Alpha.
Conclusion: Cats who live close to the ground have to keep track of horizontal, back and forth moving objects like mice, a vertical alignment improves this ability, so they narrow their pupils into a vertical-shape(see Alignment in previous post). Horses who have a higher perspective and live originally in open fields with horizons need to have a vision for grass-eating, they already have a big nasal-intersection so they narrow their pupils in a horizontal-shape, they haven’t got the natural ability to stay focused on a target like preditors. Owls have a fine balanced visual system with the characteristics of humans, narrow their eyes likewise, to a smaller circle. Although they are predators of the night they can catch mice thanks to their oblique Nasal-Alpha-Area, almost the same as cats have, see illustrated presentation:
http://www.sharp-sighted.org/index.php?option=com_content&task=view&id=26&Itemid=88