I would like to expand on what I mean by the title of this question to focus the answers.
Normally whenever a theory (e.g. General Relativity) replaces another (e.g. Newtonian Gravity) there is a correspondence requirement in some limit. However there is also normally some experimental area where the new larger theory makes predictions which are different from the older theory which made predictions of the same phenomena. This is ultimately because the newer theory has a deeper view of physics with its own structures which come into play in certain situations that the old theory didn't cover well. Additionally the newer theory will make predictions based on its novel aspects which the older theory did not consider. I know that String Theory is quite rich in this regard, but am not interested in that here. Nor am I concerned as to whether experiment has caught up, as I know that ST (and Quantum Gravity in general) is not easy to test.
So for the GR to Newtonian example an answer to this question would be: bending of light rays; Mercury perihelion movement - GR had a different results to Newton. What would not count as an answer would be new structures which GR introduces like Black Holes or even gravitational curvature per se.
So does ST have anything like Mercury perihelion movement waiting to be experimentally verified, and thus "improving" on GR within GR's own back yard?