JDMSMBACPA :
my convex edge Yari sure seems to cut better now in every media I have tried than it did before I put a convex edge on it.
Is the bevel wider than it was before, if so then cutting advantage is due to the creation of a relief, this effect could also have been seen with a flat bevel, or a hollow one, the ability for more extreme performance would follow in that order.
Buzzbait.
A convex grind generally has more steel to it than a flat or hollow grind
In general, convex grinds -> flat grinds -> hollow grinds are in that order in ability to remove metal and minimize profile. However in application this optomization is rarely carried out and thus that order can be ignored.
Usually the nature of the bevel doesn't imply anything about its obtuseness. For example hollow grinds are commonly used on cheap knives, shallow and narrow primaries which produce knives that cut poorly and take long to sharpen. This isn't due to the hollow nature of the grind.
The convex bevels used by most ABS guys are very thin, producing very high cutting ability, easily double to one, and sometimes more than the thicker flat ground v-bevels on most knives, especially the tactical ones. This again isn't due to the convex nature bevels.
You can take any flat bevel and convex it to make it thinner, which is in general what people are doing when they are reporting cutting advantages to convexing a knife. However you can also convex the bevel and make it much more obtuse and thus it will now cut a lot worse.
The only inherent advantage of convex edge bevels used in such a manner is a slight gain is smoothness of cut due to a more flowing profile - but this is a fairly small effect and easily swamped out by small changes in geometry. Anything else can easily be duplicated with multiple v-bevels, usually two is enough as was described by JJ of Razor Edge.
Now convex primary grinds are a bit different. For long blades which can take very heavy impacts, convex grinds are in general more suitable as they can handle shock better. This is mainly due to the fact that the impact will tend to "roll" around the profile instead of concentrating all the force at one spot.
You also see this effect with the edge, which is one of the reasons why durability can be significantly enhanced by the addition of a very small additional microbevel.
-Cliff