I would add another two arguments:
An img tag is good if you need to resize the image. E.g. if the original image is 100px by 100 px, and you want it to be 80px by 80px, you can set the CSS width and height of the img tag. I don't know of any good way to do this using background-image. EDIT: This can now also be done with a background-image, using the background-size CSS3 attribute.
Using background-image is good when you need to dynamically switch between sprites. E.g. if you have a button image, and you want a separate image displayed when the cursor is hovering over the element, you can use a background image containing both the normal and hover sprites, and dynamically change the background-position.
