So I have done quite a bit of reading about the issue of the "strobing effect" that some movies show more than others at 24p, and also done quite a bit of testing on my own. Here's what I've found.
It's a mix of several things.
First and foremost, how the movie was filmed is probably the biggest aspect of it. If the director of photography has used a shallow shutter angle (quick shutter speed) to capture the movie in order to make it look as crisp as possible, then every frame - even frames showing motion - will have very little blur in them, and be clear and defined. It's still obviously only 24 frames a second, but since the shutter is open for a shorter period of time during capture than normal, not a lot of light is allowed to "paint" the digital censor or physical film inside the camera, and so naturally when the camera moves, each of the 24 frames will stand out more as there is no natural "blending" in the frames that will help alleviate the feeling of jumping from one frame to the other.
The "strobing" effect is the above combined with the much higher light output and intra-scene contrast of home projection/TVs compared to most professional cinemas. To illustrate with words, if you have a dark scene with a very high contrast light in it (like headlights on a car driving at night), and this scene is also filmed with a fast shutter speed, then it's only natural that this light will appear as "strobing" when it leaves frame 15 and enters frame 16, and so on. This effect is made stronger the more light output you have at your screen, as well as the darker blackfloor and higher intrascene contrast your HT/projector is capable of.
I tried to clamp the iris all the way down, and it got a lot "better" and resembled the cinema experience more. The stuttering effect was reduced. I also tried pointing a small flashlight at the sidewall to lift the blackfloor and wash out the intrascene contrast a bit more, like the exit lights do at the cinema, and the stuttering got further alleviated to the point where it felt exactly like how it does at the cinema.
After comparing the LS10000 to the LG PF1500, there was no difference. When I brightness matched them at my screen, both showed the same amount of strobing effect during the same scenes in "Moon". Naturally the LS10000 has a lot better contrast performance, so the movement of contrast rich elements on screen will feel a bit more intense, but when filming in slow motion it's clear that there is no problem with parts of frames remaining in the next one, it just feels that way because of how much brighter the image in my HT is compared to a professional cinema, which makes each frame "stick" to the retina more.
So barring any fault with the projector keeping it from displaying 24p correctly, there is nothing "wrong" going on here, it's just simply the nature of 24fps, and 24fps when filmed with a fast shutter speed. That is why some movies feel less strenous to the eyes than others, which would be the ones filmed in a way that allows a bit of motion blur in frames depicting motion that will help the eyes between frame transitions...
Luckily Frame Interpolation exists so we can use it in movies that feel too choppy in native 24p.