We are not aware of any scientific environmental evidence that one is 'better' than the other. In fact, they are really the same material, just coming from different places along the feedstock supply chain.
Part of the problem is that some people think that pre-consumer paper is simply industrial scrap at the mill. It is not. The scrap at a paper mill is called broke, the paper material that occasionally breaks in a paper machine during the papermaking process and that is thrown back into the pulper (a big washing machine, if you like) for further recycling. Mill broke is not considered, and not claimed, as recycled content.
From the mill, the roll of paper or board is generally shipped to a converting plant that is closer to the end-market for the material. Here the actual paper or board is cut and shaped and perhaps folded and glued before being shipped onward to a distributor or maybe even the final consumer.
In the process of cutting and shaping the paper or board at the converting plant, there is always a small percentage of off-cuts, like the trim left over after a sewing pattern is cut from cloth. These off-cuts, which could be envelope clippings, corrugated cuttings or boxboard trim, are called pre-consumer because they do not go to the end-consumer. It is perfectly good material, like the sewing trim, and is sold and shipped back to a mill for recycling. It is not wasted.
Post-consumer paper or board, on the other hand, is the complete paper product ready for sale (a newspaper, writing pad, corrugated box, boxboard carton or paper bag) that ends up at a factory, supermarket, office or home and is later collected for recycling. It's also sold back to a recycling mill, just like the pre-consumer material.
There is no difference, then, in the way that pre-consumer and post-consumer paper or board is originally manufactured in a mill. It is exactly the same material (like the sewing off-cuts) with the same environmental production inputs. The only difference is that it comes back to the mill for recycling from a different place in the recovered paper feedstock supply chain. In fact, it could be argued that pre-consumer paper has a lower environmental impact overall because it travels a shorter recycling loop back to the mill.
In their rush to promote the greater use of recycled content paper, however, some environmental groups have encouraged the misleading perception that post-consumer material is somehow environmentally superior. It is not.
(Excerpt from a section on pre and post-consumer paper in Deforestation in Canada and Other Fake News).