Translation:My brother never speaks about his wife.
They are both accepted.
This is not about formal or informal. My link explains this: "Speak usually only focuses on the person who is producing the words" vs. "Talk focuses on a speaker and at least one listener, and can mean ‘have a conversation'". In light of that, "speak" fits better here since we are not saying that my brother is talking to someone; we're focusing on him. That said, they are both perfectly fine in this sentence.
Ok, I give up. I mean you have a point there. I was only insisting that "speak" is mostly used in more formal situations, like someone is giving a speech to a public. In this particular sentence both are working, (and accepted as you say). And my point is that "talk" is used more in "normal" situations, informal, family etc., so it should preferentially be used here as well. Not to mention that in the part of the US I live, no one would have used "speak" in such sentence. That said, I'm giving you a lingot for willing to discuss the issue with me.