A convex edge makes the edge of the knife stronger. The convex edge is also called an "apple seed edge" gives more strength for more difficult/harder tasks. The trade off is that it's going to behave less "sharp" than if you have a standard v-edge. Not that it's not a sharp edge just that it won't be wickedly sharp. However, it's going to last longer than a v-edge (broadly, lots of variables here).
So, for example, woodworking tools will be a v-edge because you want the sharpest possible edge. The trade-off is some of that edge will be less stable/strong over time and you'll need to re-sharpen more regularly.