The best way to tell whether a skillet or a Saute Pan is right for your recipe is to determine how much access you need to your food with a spatula while it cooks, the temperature, and the speed you plan to cook at, and how much liquid your recipe contains. Slow-cooking recipes that contain lots of liquid broths or sauces will benefit from the depth and large, flat cooking surface of a Saute Pan.
Skillets are the heavier option because of its thickness, the material used to craft it, and larger size. This extra weight allows skillets to distribute heat evenly and retain heat better, making it ideal for recipes that involve searing and braising.