Decomposition is only one metric to measure the impacts of plastic verses paper bags. There are dozens of other metrics which could also be used and could be either to favour either plastic or paper bags.
Care should be taken to only use one metric to make decisions on, as there may be other metrics which are equally inportant.
For example, if the whole world changed from plastic to paper bags, would this result in devastation of tropical and subtropical forests, in addition to tree farming/plantation forestry, to satisify the demand for paper products?
I am also sure that someone drinking dioxin contaminated water from a paper mill producing would think that plastic has a potentially lower impact. Likewise someone living and breathing air from a plastics plant.
This is why considering all metrics is important. One of the failures of government is policy decisions are often based on one metric (one interest viewpoint), without looking at the big picture or consequences of implementing the change.