I'm going to call bullshit. Farts are not an aerosol of shit. Farts are gas, not microscopic solids. Sure, as the gas passes through the shit storage, it may pick up some molecules along the way, but I would seriously doubt that it meaningfully affects the resultant odor.

Digestion processes allow bacteria to do its digestive process on whatever is consumed, allows it to react against various acids, and some of the biochemical reactions result in gases being produced, including (but not only) methane.

The gasses are then purged from your system. Some of the gasses have odors, but farts tend to be more unpleasant than belches.

Personally, I would absolutely confirm that consuming and digesting plants produce a wider variety of gasses, and specifically gasses that tend to be more offensive to our senses. Plants also take longer to digest, resulting in more rot or fermentation. Fermentation itself requires sugars, and produces gasses. Plants have sugars. There is a wider range of bacteria involved in digesting plants as well, and the sugars in plants fuel the bacteria, who metabolize portions of the plants and release their own gasses through their own digestive processes.

I once tried to use a lot of soy products because I thought I was sensitive to lactose. The soy milk especially gave me some of the worst smelling gas I can remember.

Now as someone who consumes little or no plants, I rarely have digestive gasses, and when I do, they are much more mild on odor.

No, animal meat does not "rot" in your intestines. It is largely broken down by stomach acids before it even enters the intestines, and very little waste is left at all to pass through the intestine. Think about how flesh is removed from bone using lye, and the resultant sludge solution that is largely liquid. It is overall a far more efficient digestion process, and happens quickly - 15 minutes to a couple hours. The intestinal length and volume of purely carnivorous animals is evidence of this efficiency. Our human intestines have surely grown in length and volume to adapt to our omnivorous diets, especially over the last few millenia (very recent, in evolutionary scale) with the advent of agriculture.

For more information regarding meat digestion, just look to interviews with meat-only eaters who also have ostomies, where their waste is diverted to an external bag instead of being allowed to take its normal intestinal path.