My preference for the swirling/circular motion came about mainly because I use a small (6") stone, held in my left hand (thumb at one end, a couple fingers at the other, one finger bent underneath the stone for some 'support'), while handling the blade with my right hand. The stone and blade are at such an angle that I can look directly at the edge at the 'seam' of contact with the stone. It just feels natural to 'scrub' the bevel into the stone this way, in a circular fashion. This also limits how close the edge comes to the ends of the stone, which protects my fingertips from cuts. I have managed to catch my fingers in the past, when 'slicing' across and down the length of the stone.
My homemade strop blocks are sized accordingly (about 6"), as I prefer to strop this way too.
I might prefer the slicing/drawcut method if I were using larger stones on a bench, though. Remains to be seen how that'll pan out; haven't made that investment yet.