I think it is a matter of preference. Coarser cuts will tend to stay crunchier, while finer will yield brine more readily,
I prefer a coarse cut. I quarter a cabbage and then cut in 1/4" slices. Others may prefer much thinner.
Why not try all 3 and see which you prefer?
For the wages of sin is death; but the gift of God is eternal life through Jesus Christ our Lord. Romans 6:23