Having a convex edge is a no-brainer, as far as I'm concerned. It's the toughest edge I know. It's been said that there are only 1 or 2 things a serrated knife can do that a well-sharpened plain-edged knife can't. I think the same applies to the convex edge. There are only a few applications that are better suited to other edges, while a convex edge tackles most all of what I do with my knives (exceptions being paring and filleting/skinning). It's better for woodcarving, box cutting, rope cutting, chopping, hard push-cuts, etc.
The difference is in the radius of your curve (think cross-section). If you start out with a thick piece of steel and push real hard while slack-belt grinding, you'll get a "fatter" edge (smaller radius) than if you flat grind first to a stubby edge and then slack belt the last 1/16" off.
I think some avoid the convex edge because of concerns about being able to properly sharpen and maintain it.
Sharpening and maintainence is terribly simple, just requires sandpaper and a soft-backed surface (a cushioned block, or even your hand). Restoring the finish just requires patience and the right types of sandpaper, and stropping compound.
I just finished making a CD with videos on how to sharpen this way. I took a 15" khukuri and blunted it by rubbing the edge on concrete and a metal rail. Even gave it a few dings. Within 20-30 minutes I had it back to shaving sharp using just sandpaper and a strop.
Here are a few samplers: (at low resolution - sorry)
Rubbing the knife on the concrete (did it a few more times off camera)
Scraping the rail
Proof of dullness test
Sharpening with a block 400 & 600 grit paper
Polishing by hand 1200 & 2000 grit paper, followed by a stropping by hand with green compound.
2x4 test Actually, the third time I filmed this. Had problems with the camera on the first 2 tries. You can see the paper from the first one on the chair (under the one I grabbed). No stropping or sharpening in between.
Ok....I'm off my soapbox now.
