Changing scratch direction when shaping/thinning you bevels is most important.
First like any polishing work (meaning with any tools you would use), crossing the scratch directions will allow you to properly see if you have erased all the previous scratches.
Second : scratch direction have an effect on the way you grind your bevel. What I mean is that each scratch direction will hit the surface in a certain way, touching more or less surface and allow you to give a certain shape to your bevel. That second point is often not considered but it is true tool for the people who understand it.
-Longitudinal scratches (parallel to the edge) is generally the scratch direction that will hit the most of the surface, that will give a less efficient work as the stone got to grind more material at every raw. That direction will be great to align your bevel and give a longitudinal slightly convex surface. Other issue is that it is easy to roll on shinogi with that direction as you don't work against it but parallel to it.
-Diagonal looks to be great for flattening the surface. Less surface to work so little more efficient. Good for blending different facets. Preserve shinogi. Overall the most used scratch direction to finish a knife because it is very polyvalent. I would say it is not the most pretty finish and I like to get scratch pattern more parallel to the edge for final polish.
-Perpendicular is the best direction to grind. Less surface to work with so more efficient. You can also roll on shinogi if you hit too hard. You can create a bad shape and low spots longitudinally because you're working on one spot with power and can easily overgrind (most often at the heel area). That direction is also great to create and control some convexity : you're perpendicular to the edge so you can really shape your convexity from shinogi to edge the way you want.
I use all 3 when I am shaping the bevel, depending what shape I want to create. I will work diagonal and longitudinal close to shinogi. I will work perpendicular and longitudinal close to the edge.
I cross scratch direction at every grit of my progression. When I reach natural stones I will only work in one direction (longitudinal mostly), except if I want to check some scratch I have trouble to erase or if I want perfect cleanness.