mr_fender
Axe-Master
I have thought about this a while and I've come to a conclusion. The mass of the guitar hanging from the neck adds a tension force to the neck opposite the tension force applied by the strings. This cancellation of force (complete or partial) forces the neck and strings into a long term dynamic it wasn't intended to be in. I'll go with stands or in the case.
Also, I don't know where you live but if it's in a quake zone things tend to jump off walls.
The change in tension is minimal. Use a tuner and compare the pitch of the strings when hung vs on a stand.