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The reader can assume that the sound heart and the deformed conscience refer to specific characters. I think that one characteristic of Huck is that he has a good (sound) heart, and the heart he has is one that has him helping Jim, among others. The deformed conscience could refer to a specific character (such as Pap) or it could even refer to the deformed conscience of those who prefer slavery as a way of treating people. As noted in the quote, the deformed conscience loses.
Both the "sound heart" and "deformed conscience" are refering to Huck. His character has an internal conflict between what he feels in his heart to be right (helping Jim) and the distorted morality he was indoctrinated with that justifies slavery.