Both of them are Alpha + members of the society, but this alone isn't what causes them to feel like outsiders. If anything, the superior characteristics of an Alpha + should confer a kind of inner satisfaction upon the individual. In Bernard's case, much of his dysphoria has to do (though this seems to interpret him as a superficial character) with his physical appearance. He's small and unattractive looking, and he is self-conscious about it. The whole Society is built on the principles of conformity and regularity. Bernard is a misfit not through any deliberation of thought but because he's a kind of anomaly within the system. It is not just his appearance. He seems as well to present with what we now call OCD (Obsessive Compulsive Disorder), fretting about incidental and unimportant things that should not be a concern to anyone in this "perfect world."

Helmholtz is different. He seems more of a genuine rebel than Bernard, and his consciousness of his difference from others drives him to question the role the Society expects him to play. What he has, what he's been assigned to do in the world, is fine but it isn't enough. It's as if he has the soul of an artist from the pre-dystopian period. He tells Bernard that he feels he has something inside him that he wishes to express, an "extra power" he isn't using. But given the limitations imposed upon him and everyone else, there is no outlet for it.

Both men have Otherness in their characters. It is interesting that they aren't much different from people in our own "normal" time and world who don't fit in with society, even though this future realm is supposed to be, and actually is, structured around a rigid "ideal" in which all roles are planned from "birth" and the unhappiness and tragedies of the past have been eliminated. Helmholtz and Bernard, like the story of Brave New World, are projections into the future of what is real in Huxley's, and our own, times.

Bernard Marx is a highly intelligent Alpha-Plus citizen of the World State who is disgruntled with society and is considered an outsider in his caste because of his physical appearance and unappealing personality. Unlike the other Alpha-Plus citizens, Bernard Marx is physically inferior to his peers and resembles a member of the lower castes. Bernard is significantly shorter than the other Alphas and there is even a rumor that someone accidentally spilled alcohol in his blood-surrogate, which stunted his grown.

Bernard's inferiority complex makes him a lonely, resentful man, who desires to engage in promiscuous sex with attractive women and gain the respect of his peers. As a result of his inferiority complex, Bernard develops a rare distaste for society and becomes highly critical of the World State. He even refuses to take soma and derives pleasure from not conforming. However, Bernard's attitude towards society dramatically changes once he becomes famous for being John's guardian.

Unlike Bernard, Helmholtz Watson is a well-built, attractive Alpha-Plus who is a respected lecturer at the College of Emotional Engineering. Although Helmholtz is an extremely intelligent man, he is forced to compose superficial scenarios, slogans, and hypnopædic rhymes, which he recognizes as shallow and unfulfilling. Helmholtz's intelligence is what separates him from his peers and makes him feel out of place in society. Similar to Bernard, Helmholtz also recognizes that he is different from everyone else and is displeased with the World State's shallow, meaningless society.

Bernard Marx feels out of place because he is physically different from his peers.  In the book, it is rumored that someone thought he was a member of the Gamma caste, so they put alcohol in his blood-surrogate, stunting his growth.  Regardless of the reason, Bernard possesses the intelligence of an Alpha Plus caste member, but he has the body and appearance of a lower caste member.  As a consequence, he is seen as abnormal by his peers and the lower castes.  Being ostracized, Bernard retreats into his own world, preferring to be alone or with his only friend, Helmholtz Watson. Furthermore, he criticizes his society and its values, and he feels that he is superior to his peers because he thinks freely and does not, at least in his mind, conform to the conditioning he was subjected to as a child.  However, once he returns with John the Savage, and is accepted by his peers, he revels in all the pleasures his society has to offer, completely abandoning his previous attitude towards his society.  In the end, he begs Mustapha Mond not to banish him to some remote island, away from the very society he claims to despise when we first meet him.

Helmholtz Watson feels out of place for a different reason.  Though he is physically perfect, he is too intelligent.  Life for Helmholtz is great, but he is bored.  As a writer, he feels that he is capable of great work, but he doesn't know what that work is or how to do it.  He is to a degree trapped by his conditioning.  When he meets John the Savage and hears Shakespeare for the first time, he begins to see the beauty and potential of poetry.  He also begins to realize that pain and suffering, emotions that he has never felt, are necessary to create art.  Unlike Bernard, Helmholtz readily accepts his banishment.  Given a choice of islands he would like to be sent to, he asks for one with bad weather so he can be a better writer.