The difference isn’t quality but practicality. Polyethylene is a firm, rigid foam with a closed-cell structure. It absorbs shock, returns to its original shape quickly, and provides a bit of bounce to boot. This makes it good for gym mats that are less than two inches thick. Polyurethane is a softer foam with a lot more “give” thanks to its open-cell structure. There’s more air flowing throughout the foam, and this allows the foam to absorb shock and distribute it more broadly than polyethylene. This type is good for very thick crash mats that protect against injury from hard falls and throws.