hq4x keeps angles when it should not, degrading many features in the process, and that bothers me much more than the overall change to a bit more blobbiness. Look at the outline of Bowser's horns and mouth, Toad's cap outline, Fake Sage's moustache, or Axe Battler 2 sword. The mouths of invaders are also faithfully reproduced. In the Ports icon, the cable is correctly represented, and the port itself has volume instead of becoming two planes as in hq4x. On the Keyboard one, hq4x produces a good icon, although it rounds the keys a little, while "ours" produces a non-faithful in style but nonetheless correct result. Control Panel is interesting, as "ours" looks like the hq4x version has melted, but the hq4x version produces a result that is semantically similar (piano keys, weird mouse shape, angles in letter) leading me to think the original icon is not exactly the best pixel art material (maybe due to palette constraints).
Maybe the results of "ours" aren't exactly faithful in style in some cases, but they're globally consistent, and I find the shapes semantic more truthful. As for hq4x by itself, I actually prefer the original sprites overall.
I think we're trying to optimize different functions.
For Bowser, I think hq4x is fine (the mouth needs not have a smooth contour like a human's - compare with a dinosaur or a crocodile), but you are giving more weight to the fact that the shaded part on the bottom right of the mouth is broken in several pieces, instead of being a single piece like in ours.
For Fake Sage, I think hq4x does better. A pointy moustache is fine. The "ours" version is practically melted, and hardly recognizable as an old man - it looks more like some sort of fish shaman.
For Axe Battler 2, the shaded part of the sword is jagged in hq4x, but that doesn't bother me. Same thing for the broken black outline in the leg. I am much more bothered by how "ours" messes up his face.
In general, I would say that "ours" is better at putting together some parts that are supposed to be a single line, while hq4x separates them (especially with thin shadows). But graphically, hq4x's result is much more faithful to what the sprite is supposed to represent. With "ours", everything looks like melted ink, or like it's been seen through a wet pane of glass in the rain.
It would be nice to see if it's possible to combine "ours"'s better detection of continuous shades with hq4x's better preservation of straight lines and details.
I noted the same issue with round vs sharp sections. Honestly, what this needs is a blending function, kind of like how they do intense shocks in fluid dynamics, where it would use MS's algo in areas where it detected significant roundness, and then blend into the hq4x algo in areas where there's more angular sections, like in the treasure box.
Maybe the results of "ours" aren't exactly faithful in style in some cases, but they're globally consistent, and I find the shapes semantic more truthful. As for hq4x by itself, I actually prefer the original sprites overall.