Both societies ban thought through books. As far as we know, only Mond in BNW has books, and these are locked up in a safe. It is important that the citizens of BNW not be able to think about ideas that would make them uncomfortable, make them feel: "when the individual feels, the community reels." This is dramatized in John's character. He has been introduced to Shakespeare and an entire range of thoughts and emotions that the average citizen in BNW will never be exposed to, and he is, in their view, unbalanced. In place of thought, they get electro-magnetic golf; instead of thought provoking films, they get the feelies.
Farenheit 451 might be considered the "prelude" to BNW in that they are still destroying the books that do not seem to exist in BNW. However, they have individuals who "are" books, who may be able to bring the classics back to the people, something that is very unlikely in BNW.
The goals in both societies is the same: eliminate books and feeling to control thought. You could throw 1984 in here as well ... there they have language control through Newspeak, and literature control through Pornosec.
It would be interesting to see how far we are from each of these ...