The downside, to me, of using the mousepad is, it's just too soft. 'Very light touch' is mandatory to keep from sinking too deep into the backing and over-rounding the edge or the shoulders, which then means the going will be much, much slower. Sandpaper is much less aggressive that way, when pressure is very light and the substrate is soft. Feels like sharpening on a pillow. I like using firmer surfaces, which are much more tolerant of using heavier pressure during the initial grinding stages, and even to some degree in finishing stages. Much less likely to round off the cutting edge on a firmer surface. My convex edges didn't start getting really sharp until I started transitioning to firmer backing for the sandpaper, eventually to using hardwood backing, which produced my sharpest convex edges yet.
Edit:
Sort of a double-whammy when using sandpaper on very soft backing. The softness of a mousepad will greatly exaggerate how much the paper 'rolls' or forms itself around the edge, under pressure. This makes it all the harder to minimize the rounding/blunting of the edge.