Borges was an avant-garde writer at one point. In Spanish-language poetry, the avant-garde itself tended to be a bit mediocre. It was creacionismo and ultraísmo, based on simplistic ideas about the poetic image. The idea was to invent new metaphors. Of course, Vallejo would be able to make good use of the avant-garde, and the Neruda of the Residencias was influenced by surrealism. But ultraísmo never rose to that level, in poets like Gerardo Diego.
Then Borges renounced the avant-garde. He thought that you couldn't invent new metaphors. The only valid ones are those that were universal. He began writing a lot of sonnets instead of the free verse of Fervor de Buenos Aires.
But in his prose, both his short essays and his stories, he became something else: an avant-garde writer of a different sort, in a way more imaginative than the simple search for new poetic images. He was a hero for the postmodernists and poststructuralists. He is an important translation theorist as well.
But at the same time, he never stopped being the conservative poet who had rejected the avant-garde. He wasn't two separate writers, but a single one. All the Argentine costumbrismo and the universal cosmopolitanism seemed coherent, somehow. The way for him to become one of the most original writers of all time was to embrace a theory that denies spurious notions of originality.
That is why readings of "Pierre Menard" are wrong. In actuality, the two identical texts from Cervantes are indeed identical.