I don't think Mond truly understands John's worldview, although I do believe that of all characters, he comes the closest. I think he likes to think he sees things from John's point of view, but ultimately, he and John do not see eye-to-eye. Because Mond was a radical in his youth, and because he has the right to read any literature he wants, he feels he knows John's mind. Yet his ideas about God reveal just how different the two are. Mond sees religion as irrelevant, as it is in the World State. There, science has replaced that need for a higher power. But John sees that as simply inhuman, and is horrified by the thought.
Perhaps the greatest difference in the thinking of the two men is revealed when John asks to join Helmholtz and Bernard in exile. John sees it as a chance for purification, a chance to escape this society which he feels has poisoned him. Yet Mond denies that request, saying he want to continue the experiment of a Savage living in London. Here, it's clear Mond respects John in a weird way, since John has matched Mond's mental capacity. Yet Mond still feels like he's in charge, and believes he can control John. Of course, John ends his life fully in control of his destiny, but does it to escape the insanity he sees in the culture.
I think John and Mond do agree about issues of basic human nature, but Mond feels the World State has rendered emotions other than happiness unnecessary. Whenever it seems like the two men will agree, John learns something new about London society that disgusts him. At the end of their conversation, it is clear that the two men could not be more different in their philosophies.