I think it basically has to do with what you are trying to cut, though this is probably one of the most contentious subjects in knifemaking. Whatever you hear about it, all anyone can offer is an opinion, including me.
If you are cutting wood, convex is hard to beat since it provides its own wedge to help in the cutting. Also, the sides of the blade are generally prevented by that same wedge from rubbing against the material being cut as it penetrates, thereby reducing friction. It produces the heaviest blade, removing the least amount of steel, and is the most difficult to sharpen without equipment.
If you are cutting rope or wood or most anything else for that matter, a flat grind is probably the best all around grind. The edge on a flat grind can be made convex to give you some of the advantages of the convex grind, yet the primary grind itself can be pretty fine allowing for very delicate cutting as well. While the blade is generally heavier than a hollow ground blade it can be lightened with a distal taper (ie tapering towards the point).
The hollow grind can produce the finest edge and is therefore very good for cutting flesh and most non-rigid or softer materials. It can fail utterly in the wood chopping test, because the top of the hollow grind acts like a barrier to any further penetration. Since the center of the blade is hollowed out, the overall blade weight can be the lightest without reducing the thickness of the blade's spine. Hollow ground blades are probably the easiest to sharpen over time, because the blade thickness remains thin even after the primary edge is sharpened away.
Ask most knifemakers and they will tell you that the one they best know how to grind is clearly the best to have. And most have had many years to completely rationalize that opinion...
| “A fear of weapons is a sign of retarded sexual and emotional maturity" Sigmund Freud |