This started with me wanting to share two images on Facebook to see if others could tell the difference. So I uploaded the original and optimized versions, completely forgetting that Facebook would apply its own optimization algorithm to both, making my post irrelevant. :P.
Here are two images I wanted to compare the quality of, before and after optimizing with GIMP, placed side by side using the WordPress compare image.


I couldn’t see any difference, could you? Lets look at the images individually
Unoptimized Image

Optimized Image
