I don't think it really matters which orientation. I've sent my computer through airport a few times already. I can tell you that even with the tender loving care of the typical luggage handler, my computer survived. Some long PCI cards and whatnot might come loose however. If a computer can survive that, it can survive anything. Just pack with some padding, and it should be fine. After the trip, make sure things are tight.
If you have one of those monster CPU heat sinks, I'd be worried they might come loose however.