Well now........
The side x side pic is most interesting. I did not realize that the radius's were so similar. Usually, when irons v. peeps are discussed, the peep gets a mechanical/geometric advantage because the radius (length) of the sight radius is increased. Not so in the pic comparison. Still, the aperture on the AR/M4 wins hands down on ease of use.
When understood, and used correctly, any aperture/peep is superior to the std leaf and blade iron sights, given equal visibility of each, because one of the focal planes ( or elements) involved in the sight picture is eliminated.
To correctly use a std leaf/blade, the eye (and shooter) must juggle images of the target, the front post, and the rear aperature. Correctly of course, one's focus is on the front sight, and the target and rear blur, BUT...all three elements must be kept in relation to one another.
With a peep, one of these elements is eliminated. The peep is looked "through" not "at", the eye naturally centers the front post, which is kept in focus, and the post is "applied" against the target. Two sight elements instead of three.
In my heady youth, I had no trouble shooting well with peep or irons. Now, I have run smack into "fifty something" and cannot easily juggle the three item sight picture of irons, and actually prefer a peep for that reason. The bad news is, it's only going to get worse.
With a handgun, I can hyper extend my arms and get a usable sight picture, or I can get longer barreled handguns. (or glasses, I suppose). Optics, as in scopes are another option.
On a short carbine, I'm stuck, particularly the mid sighted AK and AR's.