ArtBistro

Interesting phenomenon, but the presentation has its "thumb on the scale" in too many ways to tell how much weight to give it. This particular illustration points more to the limitations/problems of color comparison by using little "chits" in a closely grouped format. The presentation does not allow you to isolate the 2 images separately, for comparison. They need greater space between them for that to occur. Further, it causes the viewer to see them as one unit (like a painting) and as such focuses on the disparity and imbalance. The blue/green piece has much closer value & hue w/ strong and nearer equal contrast from the background - it forms its own shape. Not so with the yellow/purple piece - were its corners round, it would still not read as a unit. The tight frame also forces the "volume" of background white against the volumes of colors in the comparison.
Actually, all those corners are "rounded" by the mere pixelizing on the screen - one has larger radii than the other.
Is it a matter of: degree of rounding, figure-ground contrast, ocular tracking, object unity (Gestalt), composition & framing format, a combination, or, something else which is responsible for the apparent effect? None-the-less, its a worthy discussion needing more & different examples to clarify and understand.

I like this exercise and I agree with the author. I look at it in similiar way but perhaps I'll explain this differently. In the yellow purple example we see two shapes up against one another. But with the rounded corners you create one large shape that has been separated. Your eye follows each curve and creates one shape, because the corners are defined in your head as rounded, thus 4 corners one shape. But when you look the yellow and purple one there 16 corners that are all the same, so you see two shapes. I can't overlook the valid point that the yellow and purple contrast much more and certainly that argument has merit, but I still think this is a valid design exercise.

shouldn't the "middle corners" of the blue/green group also be rounded for your argument to work? it's not the fact that corners are rounded, it's that the 'outside' corners are the same, therefore unifying the blocks. it would work the same if the rounded corners were replaced with cutouts or star bursts. your eye sees 4 points and makes it a rectangle, the lines between them are filled in by your mind, it's called gestalt.

I think that the contrasting colors were chosen the enhance the effect.

if you used yellow and purple on the rounded corner example im pretty sure it would look just as disjointed as the one on the right.