Nothing, they are interchangeable and so mean the same thing.

Here, the would not be used in a synonymous sense. I looked up the dictionary, and was very surprised to see that it said that they are. Here, 'repertory' is only used to describe the type of a theatre company. 'Repertoire' refers to the range of pieces that someone or something can perform. - So, a repertory will perform a piece from their repertoire.