A while back I made a simple picture to show the differences between the three grinds. I just improved the picture and explained the differences a little bit on another forum and thought it would be helpful to post here as well. I know I am not the first to do this, nor the best at it, and I know this information is available elsewhere, but I think my picture makes visualizing the cutting dynamics very easy and might help some people.

Notice how the hollow grind is the thinnest in the shallow cut, and the angle it meets the material is the most acute. The flat ground blade is slightly thicker in the shallow cut, and the angle is slightly more obtuse. The convex ground blade is thicker still, and the angle is even more obtuse.
But for the deeper cut, the hollow ground blade has more thickness to make up, so not only is it just as thick as the other two (given that the blades are equally thick), but now the angle it meets the material being cut is *MORE* obtuse. The flat grind slightly less so. And the convex grind (which achieved most of its thickness early in the grind) has the most acute angle.
So for shallow cuts, the hollow grind is the best. The convex grind is the worst, and the flat grind is in the middle. As the cut deepens, the order switches.
The hollow grind has the least material behind the edge, so it will cut like a thinner knife in more shallow cuts. It is also the weakest grind. The convex grind is the beefiest, but for shallow cuts it will cut like a thick knife.
So it depends on what type of cutting you do. I have found that I do "shallow cuts" most often (by far) so hollow grinds tend to be best for me.
While the flat and convex grinds are stronger and better at deeper cuts, those two advantages are not as important as the single advantage of the hollow grind. Most of the things I cut at work are cut with just the edge and don't require a thick blade: tape on boxes, plastic strap, plastic flex wrap... If you do a lot of "deep cutting" or more heavy duty work, a flat or convex grind might be better. I also use and like flat and convex grinds. When I have to cut down a box, I like flat grinds as the whole blade has to go through the box. For most uses, you can't tell the difference.
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Feel free to expand on this explanation, or to correct anything you feel is inaccurate.

Notice how the hollow grind is the thinnest in the shallow cut, and the angle it meets the material is the most acute. The flat ground blade is slightly thicker in the shallow cut, and the angle is slightly more obtuse. The convex ground blade is thicker still, and the angle is even more obtuse.
But for the deeper cut, the hollow ground blade has more thickness to make up, so not only is it just as thick as the other two (given that the blades are equally thick), but now the angle it meets the material being cut is *MORE* obtuse. The flat grind slightly less so. And the convex grind (which achieved most of its thickness early in the grind) has the most acute angle.
So for shallow cuts, the hollow grind is the best. The convex grind is the worst, and the flat grind is in the middle. As the cut deepens, the order switches.
The hollow grind has the least material behind the edge, so it will cut like a thinner knife in more shallow cuts. It is also the weakest grind. The convex grind is the beefiest, but for shallow cuts it will cut like a thick knife.
So it depends on what type of cutting you do. I have found that I do "shallow cuts" most often (by far) so hollow grinds tend to be best for me.
While the flat and convex grinds are stronger and better at deeper cuts, those two advantages are not as important as the single advantage of the hollow grind. Most of the things I cut at work are cut with just the edge and don't require a thick blade: tape on boxes, plastic strap, plastic flex wrap... If you do a lot of "deep cutting" or more heavy duty work, a flat or convex grind might be better. I also use and like flat and convex grinds. When I have to cut down a box, I like flat grinds as the whole blade has to go through the box. For most uses, you can't tell the difference.
---
Feel free to expand on this explanation, or to correct anything you feel is inaccurate.