Which is the best way to store ball point pens: writing end down or writing end up?

neither way. lay them horizontally.

Some ball point pens have ink cartridges in them that are pressurized so that the pen will write when upside down. It doesn't matter how you store these. But, non pressurized ink cartridges (the ones that are open in the back) can end up having the ink migrate toward the back end of the cartridge. This can cause the pen to seem to run out of ink too soon or it can leak out the back. These should be stored point down in a pen holder or lain flat on their sides (like the box they come in).

I find they dry out if the writing end is up, so down!