As I'm sure you must know, discussion of the best image resizing algorithm / software package has been a real can of worms that dates even from pre-Photoshop days, ie, the late 1980's through late 1990's, when many of the algorithms were still being discussed in Computer Science classes and graduate school research. For example, a Google search on {image scaling algorithms comparison} produced over 10 million, very reasonable hits. Personally, I don't have time to discuss that enormous literature base here.
I own and use all three of the image resizing packages you mentioned, plus a couple more. My opinion is that the only way to tell which is "the winner" is to try them for yourself on the particular image that you need resized. After following this field for at least 2 decades, I find general discussions without reference to specific example images to be next to useless (at least for the better algorithms). In fact, I find that often, one algorithm will be better in one part of the image, whereas another algorithm will be better in another part of the same image. Some do better in areas with a relatively small number of well separated, sharp, well defined edges, some do better in areas where there are many, closely (and possibly regularly) spaced edges, some better where there is a more natural, fractal-like texture that needs to be interpolated. IMHO, there is absolutely nothing that beats personal experience when working in this area.
Cheers,
Tom M
PS - BTW, I have never had a problem with PhotoZoom Pro inventing unbelievable texture or edge artifacts, but I always tweak every available knob in any software I am using, LOL.
