The relative hardness of the plastic has little to do with the end result. The difference between diffusers is due to the amount of light that is let through, as well as the size and shape of the diffuser.
The soft material diffuser that you listed is convenient because it can easily be folded up and stuck in a pocket, where as the Stofen (hard) diffusers, while small, can't easily fit in your pocket. Another (dis)advantage of the soft diffusers is they typically require velcro to attach to your flash, securing it in place, but requiring semi permanent velcro.
In terms of general use, both diffusers produce about the same diffusing effect: they diffuse the light of the flash, which results in softer light. Shadows and highlights have much softer edges. As Matt's answer points out, the omnibounce changes your strobe into an omni directional light source (like the sun, or a light bulb). The folding diffuser is a directional diffuser restricting the light to a specific direction.
The Stofen diffuser is highly regarded, given it's functionality to cost. If you have the DIY inclination, consider building your own diffuser using several items found at home.