Hanging the guitar versus casing it is a 'minimal difference' issue in my mind. That is to say that any issues that may occur as a matter of storing it one way or another are pretty minor so as to not really worry about it too much.

In hanging it and wondering about things like neck to body joints, if hanging without strings, I guess an argument could be made for not doing it. However, since they would be hung with strings on; since the weight of the body is essentially less than 10lbs (example: a Les Paul averages 9lbs), the string tension counters that with 200lbs+ of counter force. Also, since a guitar represents woodworking techniques, joints have things that hold them in place like mortising, bolt-ons or through the body joining which would be pretty good counter measures themselves.

As for string corrosion, if you play with any regularity, the oils from your fingers are going to kill the strings before any air will.

However, if you keep it in a case or even out, it matters where you store it. My wife's uncle had a Gibson ES333 and could not actually keep the guitar in his house because it would not stay in tune. He had a house with no AC so particularly in the summers, it wreaked havoc on the guitar. If you keep it in a damp-ish basement in a case and things like string corrosion happen, that would make sense. Not knowing that, keeping the instrument in a light controlled, temp controlled environment are more important than case or not.

Also note: While most guitars have a polyurethane finish, if the guitar has a nitrocellulose finish, hanging might not be a good idea. The foam rubber of most hangers will 'stain' the finish of a nitro finish over time and look like a black smudge in the spot it touched. You can't get this smudge out. Know your guitar before hanging it..

So, that's my opinion and thoughts.