Hey Moose, maybe I can take up some of the slack...
I've been thinking about this a lot lately (translation... this is going to be a long post), and I think I'm coming in on the V edge side of the equation. When you get right down to it, the convex edge can be thought of as a primary bevel / micro bevel where the primary bevel is a curve that ends in a micro bevel, rather than one or two straight lines. "I think" the relative strength or advantages attributed to either style edge are probably more in the realm of theory rather than any practical difference. As far as sharpness is concerned, that comes down to the steel, the heat treat, and the final angle of the edge. As far as longevity of the edge, that comes down to what the edge is used for, the steel, the heat treat, the final angle of the edge, and the geometry of the blade. The reasons behind using primary (or convex curve) and secondary micro bevels, are just as likely to be there to overcome compromises in the steel, heat treat, or blade geometry (and its influence on usability). There are plenty of scary sharp scandi blades out there to make the point that a micro bevel isn't really necessary for a sharp or lasting edge. This doesn't mean that there aren't particular applications or geometries where each system holds an advantage over the other. I think properly executed convexing is probably better for thicker and or steeper saber ground blades, and I think thinner ground edges and most hollow ground blades probably don't benefit from convexing. I know from experience that hatchets and axes benefit from a thinning by convexing of their primary edge, often with a concaving or hollow grinding behind the leading edge, so I suppose if your knifes geometry (and intended use) has more in common with an axe than a scalpel, i.e. you're using it as a sharpened wedge, convexing may be of some benefit.
When it comes to edge maintenance, stropping is very simple and effective, and it works just as well on a V edge as a convex edge, so there is no advantage there to either system, though it might be argued that the muscle memory you will develop convexing a blade would be an advantage when stropping, at least over systems that guide the abrasives over the blade, but then that advantage can be easily overcome by incorporating the strop and medium into the system. It might also be argued that the muscle memory gained from the sandpaper mousepad system works to your disadvantage, because it is not a shallow enough angle for stropping. I've seen a fair number of sharp knives whose edges were blunted by stropping at too steep an angle. People don't realize how abrasive polishing compounds are, or how many pounds per square inch of pressure there is on the sharp edge of a knife when they're pressing it against a strop. At the wrong angle, stropping, and I suppose more generally convexing on a pliable surface can actually do more to blunt an edge than sharpen it. You can literally polish the edge right off your blade using a strop at the wrong angle.
If I were starting fresh today, and knowing what "I think" I know now, I'm sure I would not buy all the sharpening gear I've got, I'm equally sure that I'd have scary sharp edges, some of them courtesy of some neoprene and sandpaper, and some the result of some sort of clamping angle maintaining system, all of them likely honed with some leather and polishing compound. That said, I think the "average" person would get better, more consistent results sharpening with a system that maintains the proper angle and results in a V grind edge. I think one of the main advantages of our modern super steels is that the micro bevel really isn't that necessary, modern steels are strong/tough enough to have a very sharp edge with good edge retention at a single angle, perhaps a little thicker than the old primary angle, and a little thinner than the old micro bevel. They just don't need the blunting micro bevel to have good edge retention. The problem with that though, is that very few people have the fine motor control to maintain a consistent angle without a sharpening system to guide them. I really don't think people can realize the full benefit of the super steels edge retention without a mechanical sharpening aid. Now, if you're not willing to invest in a sharpening system, convexing is probably the next best answer, as intentionally convexing the edge is probably more repeatable for most of us than trying to consistently maintain the exact same angle for every pass over the abrasive.
Now, what was the question?
Erik
