I'm sorry but comparing two entirely different TV's in different resolutions to prove 4K is superior is like comparing a First-Gen 1080P LCD to a Last-Gen 1080P LCD. There are difference that noticeably increase picture fidelity that are not tied to resolution- and make a bigger impact than resolution. I already listed the main ones.

Here is the "common sense". Go outside and look at the grass. Obviously everything is real, so we aren't dealing with pixels anymore. Look at the grass at your feet- high detail, you can literally count how many blades there are in a square foot if you so desired. Now look at the horizon; can you see blades of grass at all? What about between the horizon and your feet? Much is the same with resolution. You're eyes have a biological limit in how fine of an image that can be descerned. The calculator I linked to takes the biological limits into account assuming 20/20 vision.

Sure, you might of had a TV big enough at your viewing distance that you could descern pixels with a 1080P display. I bet money the improvements in clarity were more than just resolution though- again, color gamut, viewing angles, contrast ratio, ect ect.