They are both chemically treated so the print head uses heat to make them get writing. Both are subject to the same thing that will kill the BP fastest, heat/light. Scanning them is far more effective at retaining the data and much better for the universe.

Folded "receipt" paper scans just as well as they are bar coded, and even if the stub falls off, the old gate reader that used to eat the big part is no longer in use, so the bar code works regardless if one folds it or not. The crease issue only happens on the magnetically encoded stock boarding passes, so creasing the filmsy will not do it any harm, while it will to the stock version.

The world is moving in the direction of "less packaging" to cut costs and save resources. Ticket wallets (especially the cardboard ones) are also a wasted use of resources, as is using every towel in the hotel in LAS when not needed. In fact, some airlines are encouraging the use of online PDA/smart phone BP's to cut costs and save resources.