The contributed GIF is interesting indeed. If it can demonstrate something, it will probably be that the lens brand, cost, or generation hardly matter.
I do not expect to see a lot from compressed files, but I nevertheless tried very hard to see differences *suggested*. So yes, on the picture with the wider angle, one may see *traces* of something looking like compression (whites becoming gray-ish?), given that the rest of the picture is exposed the same way in both versions. The nuance is such faint that it is not only close to irrelevant, but could be "suggested".
Worse, lenses being passive and linear devices (WRT light intensity), I do not expect them to perform any "compression" owing to glass quality or number of elements. When a compression algorithm has been at work for producing the final image, I won't point my finger at the lens anyway.
This is not to negate that lenses have their own character, as often convincingly demonstrated here, not even needing A/B comparisons. While I definitely had sympathy for the thesis exposed in the first page of the present thread, I get more and more convinced, now that we are on page 8, that it has no merits.