I believe the correct one is "They are listening to our conversation". In this "to" refer to their conversation, but I am not expert in grammar let us wait for others response.
They could be the same, but "listen in on" somehow has a sense of taking steps to do so.
If I'm at a restaurant and the table next to me has people talking loudly, I can listen to the conversation without trying very hard. However, if I'm at home and I know my husband is talking to some woman and I'm suspicious, I could pick up another extension of the phone and listen in on their convers