Downsides of plastic are the weight, condensation (although plywood and painted wood is just as bad) and difficulty to modify if required. Bonus is ease of red mite prevention and general cleaning. Insulation value may be lower but the important thing is draughts, or lack of them. To minimise condensation problems use Aubiose bedding in Winter as it absorbs a lot of moisture -it's too dusty in Summer we have found.
We have mobile coops where weight is the most important factor. Wood was the only option. They are treated with a 50:50 mix of paraffin and creosote and we have a spare coop so that it can dry for at least two weeks before the chickens go back in them -creosote fumes are toxic and vapour is given off in hot sunlight so the nest boxes are not treated.