For long guns, we generally use hard cases on hunting trips involving several people and one vehicle, cuz something WILL get banged around. Guaranteed!
When traveling alone, I prefer soft cases and try to exercise a little care...
I use foam lined hard cases for all my handguns, and, although it's bad practice, often do use them for extended storage. I first make sure the gun's clean and oiled, though, as they can cause rust as already mentioned. Some of those little dessicant packs are a good thing to keep around when using that style of case for storage.
For soft cases, be sure they're "breathable." This means some kind of fabric outer construction. I don't see as many of 'em today as I used to, but for quite a few years cheap vinyl soft cases were popular for protection from weather. My gunsmith boss loved 'em, cuz they'd hold moisture "in" as well as they did "out" and he could count on a little extra Christmas money each year. Duck hunters were always putting wet guns away in one, then forgetting to take 'em out to let everything dry as soon as they got home. Rebluing was a regular part of our income stream... and we could usually tell just by the calendar and weather when we'd be busiest!
Also watch the padding: most use foam today, which is good and bad. Good in that it protects better from bumps than older materials, but bad in that it doesn't breath as well. The thicker it is, the more you'll notice both effects.
Some case mfrs recommend against storing guns in cases, even the soft ones, but if moisture's not a problem, the fabric style has done me well. A few folks I've known over the years who use 'em for storage suggest leaving the zipper partially open for "breathing" purposes.