Answer:
Metaphorically and symbolically speaking? The conclusion is that the New South prevails over the Old South. When Stanley overcomes Blanche sexually and is the final straw in her sanity splitting, their rivalry is over, as Stanley implied when he says "we've had this coming for a long time."
Blanche represents the Old Guard in every way possible. She was born from a society that valued what bloodline you came from, and not the content of your character. She has old ideals about what is proper socially and her notions of class are outdated, which is embodied in her relationship with Stanley and her references to his "greasy" "ape-like" ways. Even though Blanche doesn't staunchly follow the rules of the world she used to thrive in, she still holds it dear to her personhood. The entire fantasy world she uses as a means to coping with the harsh realities of her life are from that very world. It's the world of her innocence before she primarily relied on her sexuality and the supposed kindness of men to get her around in life after the suicide of her husband.
Stanley represents the immigrant working class, New America in all it's brashness and brutality. He cannot stand Blanche's defunct mannerisms, and knows that her airs will get her nowhere, especially considering the fact she has no right to be self righteous because she lives the life of a hypocrite. When Blanche is being taken away in the car at the end in all her weakness and insanity, Stanley and his world belief prevails, and the Old South crumbles.