This seems to be a bone of contention in some families, akin to the over/under toilet paper debate.
This story expounds upon possible explanations for the popularity of the triangle:
http://www.npr.org/templates/transcri... but does not address the matter of halves vs. quarters.
My most frequent childhood lunch was spreadable liverwurst on firm white bread. My mother sliced it in half crosswise, then halved each rectangle lengthwise, so I had 4 logs on my plate. I have no idea why, nor have I ever seen anyone else slice a sandwich that way. Never thought to ask her when she was alive.
If you have a preference, do you know why?