Well, I think it depends on the image and how much you are resizing. If you downsize an image just a little, all that 'bicubic shaper' does is sharpen the image. If it look to jaggedy, then you should use plain 'bicubic'. If downsizing drasticly (say an avater) you might want to bicubic sharper.
As for upsizing, 'bicubic smooter' is probably a good choice because when you blow up an image it tends to get pixelly and using bicubic smoother help to smooth it out.

As for myself, I choose the one that looks best to my eye. If one look bad, I use another.