I prefer wood shavings to straw, because I think it makes the coop smell a certain way....Um maybe moldy or unfresh? (And my coop is dry.) It might just be my nose, or hayfever or whatever, but I think it's stinky.
I like the smell of the pine shavings much better, and they're easy to clean up. Sometimes in the winter (my run has roof), I put tarps around the run to block the harsh winds. Anyhow, I will put some straw in the outdoor run just to give the hens something different to scratch around in. If I put a bale in there, I let then scratch at it, and after a while, they have it all kicked around......It's just something to keep them from being bored.
I would definitely store the straw in a dry place, so you don't have to worry about mildew or mold......That can cause respiratory illnesses with chickens.
Hope this helps,
Sharon