Did you make a clipping path in one image but not the other?
How did you select the background in order to delete it?
Let's assume you used the Pen Tool* to make a workpath around the subject. Turn the workpath into a path (you can name it if you wish), then turn that into a selection (both on bottom of Paths palette), invert the selection and hit delete. That will get rid of the BG but is not a necessary step. Reinvert the path, and then make it into a clipping path (under path palette menu flyout). You will be asked to select a path to clip. If you named the path when it was made, choose that, otherwise go with the default (Path 1). Now when you bring that image with a CP into a layout program, the backgound outside the clipping path will not be visible.
* you can use any number of tools to make the path which will become the cliping path, but the Pen Tool gives the cleanest edges.