Here is the difference: the superstring theory is a reasonably good mathematical model which predicts a spacetime with 10 or 11-dimensions on purely mathematical grounds.

Not quite. More like abstractly physical gorunds...combining various symmetry principles from preceding theories.

Despite its internal self-consistency, it's not a good model of the world we live in.

Not quite. it doesn't predict a single world that is different. It predicts a landscape in which our world may be located with difficulty.