This button lets you select another object and then replaces the attribute window with a compare attribute window. In such a window the attributes ae shown on corresponding lists, all values that are equal to the other object are marked in, all differences are marked as red:
It is absolutely no problem to select an object which is not in the same directory than the one you currently examine. So objects from different servers/directories can be compared.
You could also compare object with the main window menu options Tools - Select for Compare (Left Side) and Tools - Compare with. These options are also available in the context menus of all objects.
The Compare this object with another button is not available if the attribute window is in text output mode.