You put a lot more stress on that neck joint playing the guitar and bending strings than gravity does when it's hanging there by the neck. I've certainly never seen any evidence produced that holds up the tale that a guitar hanging from its neck is a guitar neck in the process of warping.
I'll always say: the safest place for a guitar is in it's case. But if you really must put them on display, hung high up on a wall is definitely a better choice.
There are reports of some nitrocellulose finishes, like those used on older guitars or on re-issue guitars, yellowing or even rubbing off when they're left in contact with the rubber that you normally find on those guitar hangers. I know I've had one neck-hanging guitar stand discolour the finish on one of my guitars when it was left in the stand for a few weeks.
Outside the case, hung up, your instrument is also more susceptible to changes in humidity and (to some degree) temperature. Humidity has a huge impact on guitar necks and I'm wondering if this is why people think hanging guitars are being warped by the hanging -- mis-attributing the changes to the storage method and not the change in humidity? You'll want to control the humidity in your storage environment and that's easier to do in a case, but not impossible to do in a room.