Ohio won the case vs. Mapp. The Majority decision: "Our decision, founded on reason and truth, gives to the individual no more than that which the Constitution guarantees him, to the police officer no less than that to which honest law enforcement is entitled, and, to the courts, that judicial integrity so necessary in the true administration of justice." The Concurring decision: "the Fourth Amendment does not itself contain any provision expressly precluding the use of such evidence, and I am extremely doubtful that such a provision could properly be inferred from nothing more than the basic command against unreasonable searches and seizures."
This is a landmark case because it had a significant impact on how to handle Fourth Amendment rights such as in this case the right to privacy in your own home. It might have even effected the way police handle search warrant's and their accuracy in doing so.