John the savage is ridiculed by the larger new world population for his beliefs with regards to issues such as monogamy. On the other hand, Bernard is ridiculed about his beliefs with regards to issues such as love and sex. Basically, the two individuals are rebels who don’t fit within the framework of the larger society.
Bernard does not fit in because his physical features do not match those of other alphas considered to be in the same class. This likely turns him into an introvert who is not accorded similar opportunities like his peers. It is only until he comes back with John that he finds a new sense of superiority and begins to participate in activities he once criticized.
The Indians do not allow John to take part in their ritual because he is regarded as an outsider. His parents are both members of the new world, and this alienates him from the savage society. The savages do not consider him as a member of their society despite his birth on the reservation.
Their glaring difference is that John pursues the truth about the different societies while Bernard is a hypocrite who enjoys activities which he once criticized. John does not need to belong, but Bernard secretly yearns to fit in.
Bernard and John are similar in that they are both outsiders in their own societies. Bernard does not feel that he fits into the society of the World State because he is smaller than the other alphas. He also enjoys nature and being alone, making him different from all the other society members. He is made fun of by the other Alphas and Betas, and one of the only reasons Lenina will go out with him is that his differences intrigue her. John, also, does not fit into his society. He is raised by his mother on the Savage Reservation, yet he doesn't fit into either his mother's society or the Reservation. He is made fun of by the other savages.
These two characters differ in that Bernard desperately wants to fit into the society, but John does not want to become a part of either society.
John and Bernard share quite a few similarities. First, they are both conditioned (albeit in vastly different ways). Bernard is a product of the World State and therefore a product of World State conditioning--everything from biological and physical conditioning that starts within the London Hatchery, guaranteeing that whether your are an Alpha or an Epsilon, you will be satisfied within your station. Bernard's conditioning continues with his education, with the various World State mottoes/sayings that are repeated throughout the book (Community, Identity, Stability; Ending is better than Mending; Orgy Porgy). He is conditioned to use soma whenever life becomes slightly unpalatable, to believe that viviparous reproduction is taboo, and to see death as being nothing more than a means to an end for a community member who is no longer useful. Sure, Bernard may rail against some of his conditioning because of being an Alpha who doesn't fit it in because of his small stature, but he is conditioned nonetheless.
John's conditioning is less conventional, but it does exist. He's conditioned by his mother, Linda, to believe that the World State is some utopia worth returning to (though his opinion quickly changes once he gets there). He's conditioned by the savage tribe with whom he lives that promiscuity is abhorrent. This is evident when he sees the other savages' violent reaction to Linda sleeping with their mates. John also reads the complete works of Shakespeare without any guidance, using it as basically a tome by which he judges all human behavior. This "conditioning," so to speak, again solidifies his belief in monogamy and that a woman who strays from this is "an impudent strumpet." Finally, his life with the savage tribe conditions him to believe that physical suffering equates to purification, hence his behavior toward the end of the novel when he whips himself for his impure thoughts and desires for Lenina.
The biggest difference between Bernard and John is that John does strive to stand out from what is considered acceptable or normal, both in the savage reservation and within the World State. On the reservation John is ostracized because he is not of the same ethnic background as the rest of the savages. He doesn't get to take place in their rituals, yet he does so on his own. When he gets to London and realizes the "Brave New World with such people in it" is more horrifying than utopian, he questions it at every turn. Bernard, on the other hand, only questions or fights against the World State because it doesn't suit him to comply. He's an Alpha who isn't accepted by other Alphas because he is small. He's teased and talked about behind his back. Because of this he acts like a petulant teenager, breaking minor rules like not taking soma and wanting to have alone time with Lenina. Yet, when he brings John and Lina back to London, he uses Linda's connection to the Director to send him packing and save himself from being exiled, and he uses his connection to John to gain instant popularity. After that he's more than happy to be Bernard, the World State Alpha.