It depends what type of object you are modifying. If it is a nested scene, you have to open the scene and save it with a new name (the scenes are all shared). For normal resources the make unique should work, but you have to do it for everything if there is nesting. For example you can make the mesh unique, but you also have to click in the new mesh and makes it's material unique as well. Local to scene is a good way to automate this when instancing in code, without having to manually make everything unique (also make unique makes copies, so it is inefficient if you are doing it a lot).
