Sheet metal.
Any condensation which forms on sheet metal would also form on polycarbonate or wood - though on wood, it usually forms where you can't see it, between the wood and the paper. Basically, wherever the thermal break is most prominent, and the surface least vapor permissive. Sheet metal also has fewer penetrations per square foot than a traditional shingled roof, is more likely to be correctly installed by an amatuer than a traditional shingled roof, sheds snow better than a traditional shingled roof, and - assuming you leave the under eaves open (well, hardware cloth, to preserve that predator protected, weather-sheltered ventilation), any moisture which does form can run down the inside of the metal roofing to fall outside the house.
You didn't cut the ends of your rafters perpendicular with the ground? That's harder to do after the fact.
Also, where are you locating your roosting bars? Those look to be single hung windows - which will put a draft (most likely) directly on your birds when open - meaning they aren't useful ventilation in bad winter weather. No chance they will work if installed "upside down" as top open windows???
/edit SCRATCH THAT. "Duck House". Ducks don't need roosting bars. Sorry, brain was lacking caffeine. I built a raised hen house so the ducks could nest underneath. Silly me. I know this. Leave the windows as is.