It's very useful to consider the lifetime Co2 emission of a hive.
You would have to know the complete carbon footprint of the production of the raw materials used and the processing and distribution of the finished product. The wood will have a nett credit in this regard before we get started,
But because the R-value of a polyhive is so substantially better than a bare wooden hive, even in one winter season it will have saved the bees from "burning" a significant quantity of sugars. But any sugars processed into Co2, water and energy in any hive have already come from a renewable source.
I don't know which hive would last the longest but I hear that cedar goes on forever.
When both types are ultimately scrapped, whether burned or rotted away, Co2 will be released from them.
The polyhive wins when being used because it is so energy eficient for the bees. Never mind the reduced emissions...the bees will be in a better "place" in their better place.