I use both when setting a bevel. I do 20 "japanese style" strokes on both sides, then I go to circles and x strokes. I only do this on the 1k, once I move to the 2k I do 1 set of circles up and down then x strokes through the rest of the grits. I wouldn't do it on a smiling blade, but i (and this may just be in my head for all I know) use it with a blade that may have a small frown or a straight edge to "even things up" I guess. Everyone has their own process, this just works for me and is repeatable so I stick w/ it.