As you mention, the perceived distance to subjects, especially in the foreground, is very different with a panorama than it is with an ultra wide angle. This gives a different feeling to the image. I enjoy looking at a wide pano viewed at full height on the screen and scrolling left-right, I think it gives a greater sense of 'being there' than you ever get on an ultra wide.
Sometimes you don't have a lens wide enough to capture what you want. Stitching helps you work around this.
One fairly vintage example:
http://www.worldphotographyforum.com...=500&ppuser=34
I didn't own anything wider than 18mm at the time.
D.