Mustapha Mond is a Controller who helps run the World State and, therefore, is invested in the idea that happiness and security are more important than art, religion, passionate attachments, or science. As a young man, he is almost sent to exile on an island because he does genuine scientific research, an endeavor that could lead to destabilizing the state. When he is given the choice, however, between exile to pursue his science and the chance to be on the Controller's Council, he picks the Council.
In contrast, Bernard is exiled to an island. He doesn't want this and begs not to be sent away. But as Mond notes:
if he had the smallest sense, he'd understand that his punishment is really a reward. He's being sent to an island. That's to say, he's being sent to a place where he'll meet the most interesting set of men and women to be found anywhere in the world.
Bernard needs his exile, because he is too questioning of his society and too unorthodox a thinker. For example, he wants to to be alone with Lenina, hiking in the Lake District of England, a concept she can't understand because she has been conditioned to always want to be in a group. Likewise, when Bernard hovers with her alone in his helicopter over the sea water, she is scared and upset, but he craves the solitude, an anti-social attitude in his society.
Mond has the deep voice, the gravitas, and the willingness to lead what Bernard lacks. He and Bernard share high intelligence and both have inquiring minds, but Bernard is more of a misfit. He needs to be exiled so he can safely explore the unorthodox, whereas Mond is able to embrace social norms and enforce orthodoxy.