If the base stone is hard, it really doesn't matter what you do as long as you don't damage the edge by rolling it or something. You can do half strokes, x strokes, circles, etc, all of them will create a thin edge that has very nice geometry and minute shallow scratch pattern - the strop will do the rest of the work for you.
If you have some idiosyncrasy in one of the methods personally, you might find out that it doesn't work for you that well, but I personally have not been able to tell much difference with the results stone to stone when the fine stone is broken in.