Applesauce is often suggested as a baking substitute because it brings moisture and some binding. That does not make it a universal replacement for butter, oil, or eggs in every proportion.
A cake made with less fat may have a different tenderness and keeping quality. A cookie may spread differently. The apple flavor can also remain noticeable in a simple bake.
Begin with a recipe designed to use applesauce, and choose the sweetened or unsweetened type it specifies. If experimenting with a familiar recipe, make a small batch and change one component at a time.
Avoid describing the result as automatically better or healthier simply because one ingredient has a fruit name. In the kitchen, the practical question is whether the texture and flavor suit the dessert you wanted to make. Sometimes applesauce belongs in the batter; sometimes it is better served alongside.