My research and my own thoughts have brought me to the conclusion that there are two reasons why cat pupils are slits rather than circular apertures. It comes down to evolution and survival as is always the case with respect to anatomical features.
Depth of field
The first reason is spelled-out in great detail in a scientific study on the Science Advances website under the title: Why do animal eyes have pupils of different shapes?
The study explains that because the domestic cat is an ambush predator (and the word “ambush” is important in this context) they need to be able to judge distance as accurately as possible in order to assess the final pounce accurately and thereby increase their chances of a successful attack on prey.
A vertical slit in the pupil of the domestic cat’s eye provides the cat with a greater depth of field so that the image that the cat sees is sharper across a greater distance i.e. between the foreground and background. This allows the cat to use stereopsis (their binocular vision just like humans) to greater effect and to estimate distances more accurately.
It is worth adding by the way that depth of field is increased as the aperture decreases. So the reason explained above really applies to darker ambient conditions because under bright light there will be greater depth of field and the aperture type (i.e. whether it is a slit or round) is irrelevant.
Restricting light input
The domestic cat’s eye is about six times more sensitive to light than the eye of humans. In bright light, the pupil of the cat’s eye closes down to a small slit. In humans the circular pupil also closes down to create a small aperture to the same effect i.e. restricting the amount of light coming into the eye.
However, because the domestic cat’s pupil is a slit the cat can also employ their eyelid which can be pulled down across the eye like a blind going down a window to further restrict the input of light onto the retina in a nuanced and progressive way. It’s an extra level of control as to how much light is allowed to enter the eye and impact the retina. This is needed to protect the retina under bright light conditions because of its added sensitivity.
The slit pupil allows the cat to see clearly in both dark conditions – as the cat is a crepuscular hunter – and during daylight particularly in bright climates which is where the domestic cat originally comes from i.e. the African continent north of the Sahara (North African wildcat ancestor).
As expected, the vertical slit of the pupil of the domestic cat’s eye is a feature which allows the cat to survive more effectively through being able to hunt more effectively. Interestingly, the tiger has round pupils. This needs to be explained because why should a tiger have round pupils and the domestic cat have vertical slits for pupils? It appears that the reason is that the tiger does not have to depend so much on depth perception when attacking prey because they are larger. It appears that they are not so dependent upon an accurate pounce. And their range of prey items is much wider than the domestic cat so they need a greater flexibility in their method of hunting.
I think that it is probably fair to say that there is not a great difference between the image created by an eye with a slit for a pupil and an eye with a round pupil. There will be a small advantage which through evolution has been created for the domestic cat.