会話 ： usual conversation by more than 1 person (usually 2 but it could be 3 or 4) 対談： important conversation by 2 important persons (never be 3 or 4), usually before the audience. Look at the kanji 対（a pair) You can do 会話 with your friends. But you cannot 対談 with friends. 例文： なんか、楽しい会話にしたいよね～ 会話が続かなくて悩んでます。 え、大坂なおみと安室奈美恵が対談するの！？ ※　FYI: 安倍総理とロシア、プーチン大統領は、先日、モスクワで首脳会談を行いました。 It is 会談、not 対談。Probably because it is not before the audience.

会話　refers to such as everyday conversation, business conversation which means more than 2 persons talking together. 対談　is used for famous people or professional people talking about specific theme such as their special lives or economy, art, politics and so on mainly on TV , radio, and in front of the audience. So I ve never done 対談　myself.