The reason I used the general title of "Image Stabilization" was because I also had a different but related question:
Years ago, when I started recording videos, I was using digital stabilization on a camcorder and not thinking much about the issue. Then I read in "Videomaker" that for electronic image stabilization, doing it in the camcorder was no better than doing it in post. That had never occurred to me. I could not do a proper test because I did not have a pair of identical camcorders at the time, but I looked over some clips and did some frame grabs, and actually, I still could not be sure, but it looked "close enough" that I accepted the Videomaker was probably right.
That was a camcorder, and due to the limits of camcorders might not hold true of still cameras. When using a still camera, one usually has an excess of sensors to be used to construct a pixel, so by using intelligent sensor selection, a sharper image should result. But it all depends on whether the camera maker is doing it this way. Also even if it was true "years ago", by today, things could be better.
So my question is whether electronic image stabilization either in video or in still pictures is better done in camera than in post?
About the IBIS Issues:
Anyway about the video link above, as I said, I have been aware of those issues for some time, and as far as I know, they are all legitimate issues. But this has mainly to do with "motion blurring". The first problem with his criticism is that "motion blurring" is a bag of probabilities. You use higher shutter speeds and your probability of a "good enough" picture goes up. You use a monopod or a tripod and again the probability goes up. You use a longer focal length and the probability goes down. If you can, you take a few more images than you think you need and your probability goes up. And balance all this with how fussy you are. Is it "sharp enough"? Your opinion might be different than mine.
At bottom, it seems to me that a lot of professional photographers have been using IBIS and they like the results they are getting. In then end, that is what it boils down to. Am I happy with the pictures I get? So far, I have used "in lens" stabilization in my Panasonic GF3 and having used it handheld, I like the results. On the other hand, because I a not so steady in general, I usually use a tripod or monopod on my other cameras. Mostly, I can do well enough with a Yi-M1 (no stabilization at all) but even when using a monopod, I prefer some kind of stabilization. My general impression is that I do tend to get less motion blurring when using my Pentax Q-S1 which has IBIS.