We have done a lot of research into comparative Life Cycle Analyses and they all tell a similar story. Below are some interesting comparisons from a study done by RMIT on shopping bags, but the same relative findings would apply for courier/postal packaging. Our compostable bags fall into the PBAT/Starch category (highlighted in yellow).
Kraft paper is the most onerous compostable material choice in terms of green house emissions when produced, emitting 7 times the amount of PBAT/Starch based compostable material.
The same study showed Starch/PBAT mixtures to be way less needy in terms of finite resources, so you can see again paper is extremely onerous in terms of using finite resources at ~11 times the rate of Starch/PBAT. In fact we understand to produce 1mt of paper you require ~25,000 litres of water (in efficient paper plants) and 3000 litres of oil.
An overabundance of nutrients—primarily nitrates and phosphates—in water starts a process called eutrophication. Algae in the water feeds on the nutrients turning the water green. You may have heard the term 'Algal bloom' ... It can smell bad, block sunlight (which kills other living matter in the waterway), and even release toxins.
When our compostable packaging breaks down there is very little contribution to eutrophication, but when paper breaks down, it can release phosphates and nitrates. This in turn can have an adverse effect on waterways - potentially 5 times greater than a bag made of starch-PBAT.
In conclusion, there is good comparative data that puts starch based bio-resins in a very good light vs non-compostable alternatives and paper.