In a way, these opposing visions reflect the opposition between the Brotherhood and the narrator. The Brotherhood is intent on defining every aspect of life in terms of a social problem, to be solved using scientific methodology. Similarly, Wright only wants black authors to write about social problems. He thinks black literature is the only way to address these problems and sees all other genres of black literature as irrelevant and unproductive.
On the other hand, the invisible man emphasizes the complexity of humanity. He refuses to be defined as a symptom of the Brotherhood's vague social problems. The narrator is more intent on finding his own personal truth, which is why he resorts to hibernation (interestingly, Hurston also resorts to a form of hibernation towards the end of her life). Hurston is also an advocate of individualism. There were times when she didn't want to identify as black because she didn't want to be stuck in a category of people. All of her anthropological and literary work focused on black towns, where there were no black-white tensions. She was inspired by folklore and dialect, which are cultural aspects of the black community, as opposed to political.
Wright harshly criticizes Hurston for writing with "no theme, no message, no thought." This is similar to how the Brotherhood condemned the narrator for his eulogy. His speech didn't politically organize the people, and therefore was a waste of time and words. It didn't matter that the narrator had a more powerful, personal, raw message to share.
Hurston criticizes Wright for writing a "treatise on sociology" instead of a black novel. Similarly, the narrator stands up for his eulogy after the Brotherhood insults it. The narrator points out that the Brotherhood fails to include people like the zoot suiters in their methodology, just like Hurston implies that Wright fails to include black culture in his novels.
I realize that this is a biased analogy. If you agree with Wright that Hurston's novel should have a more direct political message, I'd love to hear your thoughts. Whatever your opinion is, I think the Wright/Hurston and Brotherhood/narrator conflicts have some compelling similarities. In both cases, there is a social science side and a humanity side. A systematic side and an individual side.
I do see one similarity between Wright and Hurston, however. Both believe they have a personal responsibility to write in the way they do. This at least distances Wright from the soulless nature of the Brotherhood.