Neither moral compass is inherently right or wrong. Chris Keller is guided by a sense of responsibility to the greater community, while Joe Keller is guided by a sense of responsibility to his family. Either ethic can be rightly used or abused.
In most ethical and religious systems, a sense of responsibility to a broader community is valued over a narrow sense of responsibility to family. In the Christian worldview, for example, Jesus taught that one needed to give up the claims of family to serve a higher and greater good. He understood the way taking care of family could be misused to rationalize abandoning one's responsibility to a larger community. In the play, too, Chris's ethic of sacrificing oneself or one's family for the greater communal good is depicted as the correct moral path. The way the particular situation of the play is set up, we clearly see the moral wrong in Joe sending out the faulty plane parts to protect his job and family income. In a time of war in particular, there is a heightened expectation that the family will sacrifice itself for the greater good of the community.
However, and this is the key point, an ethic of serving community over family can be abused as easily as an ethic of serving family over community. Neglecting or abusing family members, especially if they are vulnerable, is a moral wrong. For instance, Dickens satirizes Mrs. Jellyby in Bleak House. She is so obsessed with helping children in Africa that her own children are hungry and neglected. She is serving the "greater good" but in a way that harms her family. This is wrong.
Most ethical and moral systems look to a person's motive in acting: Is it self-serving? If so, we must at least be suspicious. Will the act, whether for family or society's good, be harmful in some way? Weighing these variables is important, as is balancing the needs of those closest to you against the greater good—neglecting neither one nor the other and defining "good," too, as beyond the narrowly material. Joe Keller arguably would have served his family better had he taken the economic hit through the path of serving the greater good by giving his sons a role model who was a courageous hero.