I all depends on what you are cooking and which way you like to eat your cabbage.
Here is a cabbage (above) and I am pointing to the direction of the top of the cabbage. So the bottom (where it was cut off when harvested) is on the left and you can see the thick stem part of the cabbage leaf.
I could not hold the camera and get a picture cutting the cabbage in half but I cut the cabbage in half from the top to the bottom with a large knife then I laid one half cut side down. I sliced off some cabbage from the side to show you that you will get thicker pieces of cabbage when sliced from the side.
This is what it will look like when cut from the side.
If you cut from the top instead of the side and cut thin slices you will get nice small slices of ribbon shaped cabbage.
This photo above shows where I have been slicing the cabbage from the top. Remember this cabbage was cut in half. So I am cutting on one half of the cabbage and I am slicing across the top of this half of cabbage.
I tossed these slices I cut off of the top so you can see that they make smaller ribbons and easier to eat if you are cooking steamed or boiled cabbage. If you had cut off from the side the pieces would have been different shapes.
This is just a tip from Grandma Donna.