The simple answer is that 会話 is the more common word to describe a dialogue like an everyday conversation, for example, about your day or such. In the context that Genki presents this word, it is a neutral dialogue between two people.
対話, however, is a slightly more advanced term with a different connotation; it is also dialogue but in the context of an argument, not the kind where people are arguing with each other, but where people discuss a topic with contexts and deliberation.
Breaking down the kanji to understand:
会話 -- dialogue
会 -- meeting, gathering, party
話 -- tale, talk
対話 -- dialogue
対 -- vis-a-vis, opposite, even
話 -- tale, talk