These corners are so close that they're going to have no practical difference when 3D printing them, the maximum deviation between G1 and G3 is only 0.1mm. You need to exaggerate the effect much more to show the difference.
> G3 continuous corners mean that the print head experiences smooth acceleration while printing such corners.
Axial acceleration is the key here, not just acceleration, that however does not matter if the controller does not output feedrate profiles with smooth acceleration to go along with it.
> the maximum deviation between G1 and G3 is only 0.1mm. You need to exaggerate the effect much more to show the difference.
Even if the difference is small, it can be very visible because of how light is scattered on the surface. This causes visible transitions when the splines intersect the sides. Depending on what you do, it might or might not matter, but there is a visible difference.
I cannot test, but I would think that it would also be felt with the fingers. Of course, it matters only if the surface is smooth enough in the first place.
It seems small in absolute terms, but it's suprisingly visible, even to "normal" people, which was the entire point of making a physical object!
I gave that object to a dozen people without explanation. Only one of them was a designer. All of them preferred G3 after comparing corners by look and touch for a few seconds. Honestly, I was surprised that it was this unanimous; I deliberately made the difference small.
> the maximum deviation between G1 and G3 is only 0.1mm
In a small 100x100mm box, with a 12mm fillet, G1/G2/G3 corners already have a visible 0.5mm difference. What gives it away is the lack of a hard transition between the flat surface and the corner, that's very noticeable on a reflective surface.
On the mechanical side, I think the effect they refer to also comes down to that transition line - going from a straight line immediately into a curve (G1) which adds lateral forces, vs easing into that curve over a few more steps which avoids jerking the print head.