No, hq4x is still better on almost all of them. Microsoft's makes everything too round and blobby. It pretty much only works really well when everything is round, like in Boo. But look at what it does to the Golden Axe characters' faces.
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.
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.