_,,,^..^,,,_ said:

As you can see, images are really close in quality, right? But, according to PSNR, the first has only 3/4th quality of the second, while using only our eyes, we should disagree, as we think quality is really close...

I don't know... When I first looked at these two images (without reading any of the text), the second one definitely looked off. Inspecting closer the quality was certainly worse by an obvious amount (at least to my eyes).

I don't really know much about PSNR vs. SSIM, but I would venture a guess that if these images were in motion, it would be much more difficult to tell the difference between the two compression levels?