These types of sponges are very effective for cleaning grills, some outdoor furniture, and cookware with backed-on food.
Abrasive sponges are more expensive than simple cellulose sponges, but they power through tough tasks easily.
A lot of these sponges are color coded according to their level of toughness. Unfortunately, there is no standard between companies and even in their own brands for the color coded system. Your best bet is to carefully read the packaging to determine if the abrasive sponge is right for your surfaces.