In my older coop, a real one, I have cement for a floor. I use pine shavings on top of it. I was a straw/hay guy up until I got convinced by a lady at the local farm store to use shavings. I now find them the litter of choice by far. Straw and Hay are like putting gravel in a wet hole, you can stand on top of it and be dry, but all the water is still in there. Shavings seem to draw up or wick any moisture away and from there it leaves the coop as vapor I suppose. The shavings seem to dry out in normal use at any rate.
Anyway cement and shavings are what I would use in all of my buildings, were I given a choice.
Best to you in your choice(s),
RJ