In Julius Caesar, after they realize that they are defeated and will be captured and humiliated, in Roman fashion Brutus and Cassius each have their servants hold their swords while they run themselves upon them. Such a death is considered nobler by the Romans. Such is also the case with the "noble savage," John, well-read in the works of Shakespeare, and who literally lives Shakespeare as a means of creating a reality for himself (in his last converstaion with Mustapha Mond, John uses Hamlet's words). For, he, too, realizes that he has been defeated in his attempt at escape since it is really just another experiment for Mustapha Mond. So, rather than be an exhibit for the residents of the New World and be humiliated as though he is part of a circus entertainment, John takes his exit from the his defilement with Lena and the tragedy that has become his life. His act is not an act of weakness. Were he weak, he could just take soma and live out his life in a lifeless state. Or, he could surrender to Mond and the state of the New World and conform. Instead, he wreaks his final act of penance for succumbing to his physical urges after the woman resembling Lena arrives out of a helicopter and the ensuing orgy from which he awakens: "Oh, my God! my God!"
You ask for people to argue both of the points of view. I will argue that John's suicide is a sign of feebleness. The reasoning here would be that John, if he were truly strong, would not have given up on life.
John hates the way that the brave new world operates. He hates everything about it because he feels that it robs him of his humanity. However, this does not mean that he has to kill himself. If he were stronger, would he not find some way to fight against the system? Would he not figure out a way to try to make things better, to support people like Helmholtz who are trying to change things?
It seems that suicide in the face of problems is inherently feeble. If John were stronger, he could have found a way to resist rather than giving in.