Your version at the left has the corner replaced by a fourth of circle. There's an abrupt change from straight horizontal or vertical line to circle. Human sight recognizes a step in the curvature, no matter the direction changes still smoothly- except it doesn't because practical renderings are made of pixels, so also the direction has a step, but in high res that's neglible.
(not asked, but if a railway had such curves, people would notice an unpleasant sideways thump when the curve starts and the centrifugal force jumps abruptly ON)
Any method which replaces line+circular curve with something where the curvature changes smoothly will fix it. Here's one example in Inkscape:

Both of these are rounded squares, but the blue one is converted to path (=bezier curve) and there's new nodes inserted to the midpoints of the sides
The next step is to delete all original nodes and to stretch the midpoint node handles to equally long and strictly horizontal and vertical. The result:

In Illustrator you can do the same differently:

Start with a square which is rotated exactly 45 degrees with Object > Transform > Rotate
Draw a square (red) around the rotated square, it will snap easily if you have snap to points and smart guides ON
With the anchor type conversion tool drag the handles of the rotated square to the corners of the red square