In Huxley's novel, Brave New World, which is more important, freedom or happiness? How is this shown throughout the novel?

As with any question, the answer depends on an interpretation of words, especially in this case, because both "freedom" and "happiness" are relative terms and can be defined differently by different people. Our judgement of the dystopia of Brave New World, and the importance of freedom and happiness, must stem from our own expectations, in our current lives, of what is necessary or even possible in creating a life that is worth living and is satisfactory to us.
In Huxley's future society most of the "messiness" of the natural world has been eliminated by scientific planning, and by drugs. To us, and to John, the "Savage," having not known this sort of "perfection," it is unnatural and undesirable. If it were what we had been brought up in, however—if it were all we knew—"imperfection" would then be undesirable, and impossible to live with. The dystopian residents, if suddenly plunged into a world where there was no soma and no rigid organization of society through genetic planning, would probably go crazy. We, in our present age, brought up with egalitarian ideals, think (correctly) that it's barbaric to have a society in which through eugenics, selective breeding, every human being is given an in vitro start which predetermines his or her intelligence level and every other characteristic, which will thus limit that person's choices in the world, and thus, their freedom.
Obviously, in the view of the state managers and scientists who control the society of Brave New World, "happiness," as they define it, is the most important thing. Most of us, in our world, if forced to make a choice, would say that "freedom" is not only more important, but that happiness is not possible without freedom. In Brave New World, this is where the issue of drugs comes into play. Though the use of soma seems largely to be described as an incidental kind of thing, it basically controls people's reactions and creates a kind of forced happiness. But given that the population at large have no expectations beyond this controlled society as they know it, it really may not make that much difference whether they use drugs or not. John, the Savage, because he comes from the obsolete, primitive world that has managed to survive whatever apocalypse has resulted in the dystopia, can't cope with this sort of mechanized happiness, and the result, tragically, is his suicide.