Ultimately, there are similarities: they're both dystopias, concerning future-states where human freedom has been curtailed. Brave New World is more of a false-utopia, however, where comfort and hedonism has replaced freedom, and where people live largely pleasant lives, albeit lives void of meaning and authentic human engagement. It is a society shaped by psychological manipulation, via the use of drugs and large-scale conditioning. Orwell's dystopia, on the other hand, utilizes tools of oppression which Huxley's world does not require, with its much subtler forms of social control.

In addition, I also think it's worth discussing the contrasts between Mustapha Mond (the World Controller) and O'Brien (a member of the Inner Party). In these two very different individuals, we find that these two dystopias have been shaped by very different motivations. In Brave New World, we find a world that's been shaped by an extreme form of utilitarianism, where all his been sacrificed to the end of achieving comfort and stability. This, one can say, is the real message of Brave New World: that utopianism is ultimately impoverishing, and leads to a dead end. O'Brien, on the other hand, voices a very different motivation. In 1984, we find the Inner Party is motivated by nothing other than the desire to assert power for its own sake. Thus, we have the famous quote, "imagine a boot stamping on a human face—forever": that's the goal to which the party operates: domination is the end in itself.

In each book, people have learned to survive by basically checking out.  They are not interested in confronting their society’s problems.  Instead, they take Soma or keep their head down and swallow the government’s mumbo jumbo.  No one faces reality.

Both share the theme of enslavement versus free will. In both societies, the common citizens are reduced to whatever the ruling elite wants them to be, while the elite continue to retain their own free will. The difference in theme are that in 1984 the elite emphasizes the labor of the common citizen, counting on their lack of intelligence, while in Brave New World the elite sacrifice creativity, spontaneity, individuality and imagination for a controlled society, though they court the intellect of the Alphas by showing them the margins of "primitive" cultures.

I would say that the main theme that these two books have in common is that people cannot create a perfect world.  In both books, you have governments that have tried to create utopia in some sense.  They have tried to plan their society to be just the way they want it.  In both cases, they have ended up creating something horrible.