I don't know which way is best. You should also consider the wholesalers who all store their cues laying down, in boxes that they came in or in wooden bins or on shelves. I have known collectors who do both ways. One of my friends had them in a safe in drawers. I personally prefer to store my cues vertically because I think it's more natural for cues to be standing up. I keep them either in a rack or in my cases standing up at home.
But my playing cues live in the car, laying flat in the case. Our cases are padded inside though so the cue is supported by padding.
I don't think that anyone can prove one way or the other that laying cues horizontally is bad for them. Kao Kao has tens of thousands of cues in their warehouse and I have often gone there to buy a cue and to date I have never, not once picked a warped cue out of the box.