I personally use microbevels, and don't care to do convex sharpening. However, the truth of it is unless you are using a jig when you freehand an edge there will be some sort of convexing in your edge due to biomechanics. If you are really good the convexing will be minimal, but it is there. Anyway, for me it only takes 5-10 passes per grit on a microbevel to get a knife completely sharp, which saves me a ton of time. When I first rebevel a knife to a thin backbevel it takes a little time, though my DMT XX Coarse hogs off steel super fast, then at that point I refine the edge up to 8000 grit to make it presentable (and sharp), then microbevel at 8000 grit and beyond to finish. Subsequent sharpenings go very fast at the microbevel angle, and I find I get maybe 5 or so sharpenings (sometimes more) before the microbevel thickens and I have to reset the backbevel. With my DMT stones that process is pretty quick.
Convex edges can be strong or weak depending on how thin you go, just like a v bevel with microbevel. I personally have never done convex sharpening, but there are lots of good sharpeners out there that swear by it. It certainly seems simple enough to put sandpaper on a mousepad to sharpen, and I've seen plenty of great pics of the sharpness you can achieve. I say sharpen however you find it easiest to get a good, durable edge that you can get sharp. I have had great results with microbevels, but I certainly wouldn't try to talk you out of convex sharpening. I personally think microbevels are extremely fast to resharpen and I know they have great cutting ability and edge retention when you get the appropriate angles for the steel and usage you are dealing with. Convexing you would have to find that same balance, and I'm not sure how fast resharpening is (I hear it's fast), but until you try sharpening each way you won't know what works best for you. Since a mousepad and sandpaper is cheap convexing might be a great way to start sharpening (some stones get pretty expensive).
Mike
