This question, like so many others, hinges on what "freer" means. If you are a determinist/behaviorist, perhaps there is no such thing as freedom, so the question is irrelevant. You might want to read B.F. Skinner's "Beyond Freedom and Dignity."
To my way of thinking, John is freer because he is aware of a larger range of options than the citizens of BNW. They know only what they are programmed to know (although the Island indicates that the programming is less than perfect), so there is little to no chance that they are "free." The real question is "Does John's wider knowledge really provide a wider range of choices than those of the citizenry?" Does his upbringing give him a seeming range of choices that are easier for us to identify with, but give him a very small range of options because of his "formation"?
I know that he is the character that 'seems' freer, but I'm not sure that he really is. I do suspect, however, that his version freedom is much more attractive to us than the alternative.
John was raised by his mother on an Indian reservation in New Mexico. His view of civilization is based on the stories his mother told him, but his view of what it means to be human is based on the Shakespearean plays he read, which was the only book he had access to while growing up. He is called the Savage because the world he grew up in is considered to be primitive by those in the civilized world. By most of our standards today, we would consider John to be freer than those in the civilized society of the brave new world. He's free to think and to have knowledge that those in civilized society don't have. He feels emotions, but the World Controllers have taken emotion, including pain, away from the people. They have taken truth, beauty, art, and God out of society, all the things that make people think and feel. John can't understand how anyone can live like this and knows he has no place in the brave new world.
A fine question! I would say that yes, he is freer, but not completely free, and the reason is the second question you ask. The members of the state in Brave New World are consciously, methodically, and rationally conditioned. They are shaped by hypnotic slogans and drugs, as well as peer pressure, and the result markedly limits their thought. John, by contrast, is conditioned by the same sort of forces that shape you and me. He's shaped by prior generations, by the context into which he's born, the accident of family, and by literature. He is conditioned, but irregularly. This leaves gaps for pockets of freedom.