I have both styles. I definitely think that my convex are sharper, and much much easier to maintain than my v-grinds. I usually just strop them a few times on each side and they are back to being hair popping sharp. I can do a proper convex edge profile on sand paper and mousepad, and then maintain it on a strop. With a v-grind, I have to use a system like my lansky, or Smith ceramic/diamond hone. Takes much longer.
If you damage a convex edge, you can take most of the damage out by steeling, or using sandpaper/mousepad to remove more if necessary to fix, etc. You can also use stones on a convex edge, as long as you don't keep the angle exactly the same every time (which is actually hard for most people to do freehand) it will maintain it's convex nature. When I originally did one of my knives convex, I first took the reverse curve out of the knife with sandpaper on a glass sheet. Even though there was no give to the glass, and it was perfectly flat like a stone, it naturally began a convex process because of the natural variation in every hand movement.
As to v grind or convex being sharper, you can get either stupid sharp if you do it right. Convex grinds can be thicker or thinner than a v grind, and vice versa, it is all in what angle you choose to use. My fixed sharpening system has a settings ranging from razor to axe/cleaver angle. The same goes for convex, you can use a very obtuse angle for a tougher edge, or use a lower angle for a thinner edge.
I am just really loving every convex edge I have ever had, but until recently hand no idea how super easy they were maintain.