Harmy said:

I never made any adjustments to the Tarkin picture besides the resizing. But the picture posted here recently is a heavily compressed version of the original picture, which I can't find either.

Also, looking at those pictures CatBus posted, especially switching between them at full resolution, you can definitelly see a difference in sharpness on a big screen but not really in detail - I almost find the 720p ones more pleasing to the eye, because they have all the detail but they don't look so artificially sharpened.

The difference would of course be even less perceivable in movement.

Well, a lot of people would add a hint of sharpening when downscaling to counteract that softening effect, but my examples were simple downscales without any other filtering. I agree the 1080p images look artificially sharp, but I think the 720p images maybe go too far in the other direction.