Submerging it in water made a huge difference. Maybe some chemical engineer can confirm my layman observation.
Also, when I try to squat with my feet flat on the floor as shown in that video, I invariably fall over backwards.
I also fall over when I try to squat flat on my heels. Friends who do yoga and friends from countries with squat toilets have no trouble with it though. All children under about 10 years old can squat just fine. Lesson: get your kids a squat toilet if you want them to have standard human levels of ankle flexibility when they grow up (also very helpful for improving jumping skill, if they plan to ever play sports). ;)
Considering the kind of odor we are talking about here, I just don't think the difference is really that huge because when it stinks it stinks, and it pretty much always stinks.
Tho, how to quantify odor sounds like an interesting question.
Isn't filtering volatiles through water part of the logic of a water pipe/bong/hookah?
For the last few months I've been using a urine-diverting style waterless toilet, where the solids land in a bucket with dirt. This means the solids are uncovered until completion, when more dirt gets poured over. The dietary feedback in this arrangement can be brutal, odor being a significant component until covered.
It's a weird surprise, suddenly getting touched there when not expecting it. Then there is an additional body part that needs cleaning.
You get the odor anyway, that difference is quite negligible, but the "shit shelf" also serves a purpose: It "breaks up" the log by curling it and thus prevents clogging the toilet/the log getting stuck. Which, depending on the size and consistency of it, can happen quite often.
These toilets also ain't universal in Germany, the one in my flat sadly doesn't have a "shit shelf", which leads to the situation that I sometimes (after eating too much for a while) have to flush several times until it's gone. That's not just a waste of water, it's a rather nasty process having to go through.
Squatting toilets also ain't reserved to Turkey, many Asian countries have them. Using them depends a lot on technique, here's a rather humorous tutorial [0].
I can see the advantage of them as minimizing skin contact with the toilet's surface, which depending on the hygienic state of the toilet might be quite preferable.
[0] https://www.youtube.com/watch?v=fCTKDn3Q8xQ