Bernard Marx is exiled to an island at the end ofBrave New Worldbecause he can't function happily in the society that dominates. Marx is a social outcast because he is an Alpha who is too small for his social class. When he figures out a way to find success in his career and in his social life (through exploiting John) he becomes greedy and more selfish than before. When that falls apart, he mentally can't go back to the way things were because that would be like admitting failure; and, failure was everything he wanted to avoid.
Helmholtz, on the other hand is a product of the new ways of thinking, but he will always feel unsatisfied with his world because he is too smart for it. He also has a creative and sensitive side that isn't allowed to be expressed in the New World because everything is about immediate gratification rather than the development of art or poetry. The New World, therefore, has nothing more to offer these two; especially after they obtain so much knowledge from Mustafa Mond in chapter 17 as the whole philosophy of societ is unveiled.
Hmmmm, not too much to add to the above answer except that the ending of Brave New World is the opposite for these two characters. Helmholtz is the citizen while Bernard is the exile.
Helmholtz would be considered the New World "success story" of the novel: conforming to the new state, but always remaining unsatisfied. How do we know he has conformed? Helmholtz laughs at the very idea of family: something that is antiquated. Helmholtz is a product of this "brave new world." Why is he unsatisfied? Helmholtz is more intelligent than his world gives him credit for. Poetry and sentiment isn't expressible in this world of instant gratification.
You read and you’re pierced. That’s one of the things I try to teach my students ― how to write piercingly. But what on earth’s the good of being pierced by an article about a Community Sing, or the latest improvement in scent organs? ... Can you say something about nothing? That’s what it finally boils down to. I try and I try.
Even though he is a model citizen at the end of the story, there is a note of disillusionment at the end because Helmholtz can never truly be happy with his literary talents and sensitivity stifled.At the end of the story, Bernard proves to be Helmholtz's polar opposite. Why? He is NOT the success story of the state in that Bernard has to be exiled to an island due to his own unrest in the society! Bernard becomes a social pariah due to his thoughts that the "brave new world" has always tried to suppress (but was unable to in Bernard). Bernard begins to criticize outwardly and desire those same things inwardly, thus being a hypocrite. His unrest can be seen in this short conversation with Lenina:
“But, Bernard, you're saying the most awful things."
"Don't you wish you were free, Lenina?"
"I don't know what you mean. I am free. Free to have the most wonderful time. Everybody's happy nowadays."
Thus, as you can see, by the end of the novel, Helmoltz and Bernard are shown to be complete opposites in regards to how they accept (or reject) their society and how their society accepts (or rejects) them.