I've both types of steel in a few knives (Lionsteel and Fallkniven) both are fine although not a direct comparison as the Fallknivens are convex ground and I leave my Lionsteel knives with a normal primary bevel. The LS sleipner holds an edge for a long time and is easy to sharpen ime it holds an edge longer than the Lam. Cos. Neither have chipped on me when working with wood and appropriate mediums and both steels have been more than tough enough, again on woods ranging from pine to hard narly woods.
I don't cut cardboard, sissal rope or any of the mediums that seem to be commonly used to test edge retention with these knives, I'll use an appropriate steel for more abrasive medium.
I do love the Hattori blades though, and both are extremely easy to sharpen to a very fine edge.