OK, I'm talking bushcraft and not surgery here:
A convex edge is never as pointy (sharp) as a v-edge at the same angle, yet it has less resistance in cutting, making it cut pretty much the same; but not in surgery or shaving though.
The main drawback of v-edges is the shoulder between the edge and the primary grind. Yes, one can take it down and have a really sharp v-edge with very little shoulders, but then the convex zero grind or even the convex edge excels, as it won't be as pointy (minimizing edge roll and chipping) and it has less friction. Also, I often find that I slip on the shoulder of a v-edge while carving wood, whereas with a convex or scandi I don't. Basically, if you take a convex, a v-edge and a scandi to the same angle of your average scandi, then the convex won't be as sharp (pointy) as the other two, but it will have less resistance in the cut and therefor act as if it was just as sharp, but they'll all cut with different characteristics, i.e. the wood slicings will curve differently for each knife. I pretty much convex everything because it offers a less acute edge, which won't roll as easily yet it feels just as sharp as equivalent angled knives while cutting wood, because it has a streamlined geometry. Also, I like the look of a shiny zero ground blade.