Which is more befitting: to listen to the preacher's lesson in the mosque between the Adhan and the Iqamah, or to continue reciting the Qur'an?

Reading the Quran and listening to admonition are both good. It is permissible for someone reading the Quran in the mosque to continue reading if a preacher stands up, as long as there is no disturbance to the preacher or the listeners. It is also permissible for him to stop reading and listen to the admonition. He should choose what is most beneficial and advantageous for him.