To directly answer the question: no, I don't think either model is plausible. However.... We'll get to however momentarily.
We need to start with how optics work
The reason the pupil doesn't move is that light passing through the pupil (and the lens) is cast onto the entire back surface of the eye. All rods and cones are exposed. Pupil dilation limits the intensity of light, but doesn't change where it falls on the back of the eye. This is efficient! All the rods and cones are in use and the brain is processing information from all of them.
A moving pupil means either a very complex set of optics to keep the image in focus and cast upon the only set of rods and cones, or a forest of rods and cones only some of which are exposed to light at any given time. That means a complex brain that knows when to interpret information from what cones, or one that knows what to do with all the black that contains a roving circle of light. This is a problem for evolution, which tends to favor simplicity over complexity. Human eyesight, as complex as it is, is mechanically (i.e., optically) elegant.
Let's add the fact that the human eye is spherical. One reason why is that optically the image cast by the lens is less distorted against the curved background than it would be on a flat or, per your images, a surface that changes angles several times.
Finally, an eye is an eye
One more point before I talk about a potential alternative (the "however..."): one can claim that humans have moving pupils because when the eye moves, the pupil moves with it. Moving a pupil on a flat surface buys you nothing. The surface must have some curvature. Moving a pupil along a curved surface (within an "eye") is just an eye and we're just erasing names and penciling them in elsewhere. In short, you haven't invented an eye with a moving pupil, you've simply created an eye.
What can we do about this?
I love your reference to turning the head like an owl. Owls turn their heads to focus their hearing. In fact, that beautiful plumage around their eyes is intentionally shaped by evolution to funnel sound to the ears.
What we need is a way to move a "normal sized eye" around in a way that lets you preserve the large-eye look while maintaining a purpose.
Let's start with the skin around a chameleon's eye:
For a chameleon, all that extra flesh serves the purpose of allowing the smaller and spherical eye to be positioned for vision across nearly 360°. But we're not going to use it to reposition the eyeball, we're going to use that kind of flesh to do something useful with light.
Humans, thanks to the ability to rotate the eyeball, can see about 200° horizontally. But for some reason (I'm voting for a thicker skull to take a better beating when defending against predators, but I'm guessing outrageously about your creature, or maybe the eyeballs are very, very small) the eyeballs in your creature(s) want to move very, very little. This seriously limits the value of peripheral vision.
The solution? A skull structure that places the eyes at the center of a wide field with limited muscular control. Surrounding the eyes is a stretch of skin (scales, feathers...) flat or slightly concave. Color them light if you want to improve peripheral vision. Color them dark if you want to reduce glare and increase efficiency. Either way, the creature must turn its head like an owl to get clear views around itself.
And if you really want to have fun, use nictitating lids for lubrication and that big field of skin for protection. Muscles don't rotate the eyeballs. Instead, they draw the eye deeper into that thick skull, all the while pulling that skin very nearly over the top of the eye. The result is a highly protected eyeball with just enough view through that pulled-in skin to see directly in front of the creature. And since we're dealing with a creature that needs to turn to see around itself anyway, that'd be a great way to both protect the eyes and remain very focused on whatever it is that's attacking you.
If you insist on creating actual eyes...
I assume what you want is the wide-eye white look. That's hard to achieve. Eyelids exist to protect the eyes from wind or bright light. Tears exist to lubricate and protect. If you don't use a large field of "skin" as I've suggested, then you need lids and tears for your very large eyes. Lids are problematic because muscles must pull them into large folds. Tears are less of a problem, other than your creatures would be tearing to excess all the time due to the much higher evaporation. But let's ignore those things.
What you could have is a eye that's curved to a wide arc (such as a very large eye would have) on one side (the pupil side) and curved to a much smaller (or, should I say, "flatter") arc for the back. It's the smooth shape the optics needs (remember, discontinuities are bad for optics). In other words, it's mostly flat in front and spherical in back. Call it half an eyeball.
The eye isn't held in place by muscles, like human eyes are, but by something more like ligament material. The is necessary because the larger eyes taking less space require something more capable of holding the eye in p;ace. The problem with ligament material is, compared to muscles, it's inflexible and slow. This requires the head to swivel to see more than literally what's in front of you
But it does move just a bit... and there's no "moving pupil," which is very hard to rationalize.
Final word about a word: why "is this plausible?" is a bad question here
Asking if something is plausible can mean two things, and we don't know which one it is. You could be asking if your idea can factually exist in the Real World.
Second, the question is almost always an invitation to review an idea. For that, you must use the review-my-idea tag because we had to craft a policy that would allow for review questions, which are otherwise contrary to Stack Exchange's rules. Be sure to carefully read the wiki because that tag also has rules that must be followed.
Why do I bring this up? Because whether or not something is "plausible" within the world of science as we understand it today (and that's very important to remember) isn't worldbuilding. There isn't a gang of rabid scientists waiting to jump you in a dark alley because you've proposed something we haven't seen before and they're uncomfortable coloring outside the proverbial box. And if you're looking for a review of your idea, the review-my-idea tag and its rules are the correct way to do it.
I think you have a good idea and only need to work out some details.
(Sorry if it's crap)
(Again, sorry if it's crap)
