All of my korean friends have always tried to tell me its about taste and texture, though everyone's explaination at that point starts to become very subjective.
What I have observed is cutting into quarters or halves just makes it so each time you serve the Kimchi you have all the expected parts of your cabbage head. The crunchy stemmy bits, the balanced 50/50 stem/leaves, and leafy bits. Every time i have pre chopped, the bottom of the jar ends up being all of the leafy parts and texturally the kimchi is not as good towards the end of the Jar.