karrow,
The KME is several advantages of the Lansky, and the clamp jaws may be one. The pic isn't good, but you can make out the "notches" I was talking about. They work fine on the back of something relatively square like the back of a knife blade, but they're only about a 1/16th deep. Go past that and things have a tendency to move in the jaws, especially if you can't seat it deep or the contact area isn't uniform because the surface isn't completely flat. The KME is more stable and consistent due to guide rod containment. Plus it has full range of angle adjustment as opposed to preset slots. The beauty of the Lansky is I've been using one for about 40 yrs. at less than half the cost.