As far as "Inside My Love,", Minnie Riperton's original was good, but Trina Broussard's version was just as good, if not better (mainly because of the backing music, because vocally, they sound very similar).
Another example:
Dr. Buzzard's Original Savannah Band
Queen Latifah
Here, Queen Latifah did extremely well (shocked the hell out of me when I first heard it), but the musicians backing her sounded excellent as well (probably due to producing). Because of the combination, the Queen's version was much better.