Reading Qur'aan and listening to it are both righteous deeds for which the Muslim will be rewarded.
The Prophet (blessings and peace of Allah be upon him) sometimes liked to listen to Qur'aan from other people.
Al-Bukhaari (4582 and 5049) and Muslim (800) narrated from ‘Abd-Allaah ibn Mas’ood (may Allah be pleased with him) that he said: The Messenger of Allaah (blessings and peace of Allah upon him) said to me: “Recite the Qur’aan to me.” I said: O Messenger of Allaah, should I recite to you when it was revealed to you? He said: “I like to hear it from someone else.” So I recited al-Nisa’, and when I reached the verse, “How (will it be) then, when We bring from each nation a witness and We bring you (O Muhammad صلى الله عليه وسلم) as a witness against these people?” [al-Nisa’ 4:41], I raised my head, or a man who was beside me nudged me and I raised my head, and I saw his tears flowing..
So what is best is to do that which is in his best interests and will have the best effect on him, whether it is reading or listening, because the purpose of reading is to ponder and understand the meanings and act upon what is indicated by the Book of Allah, as Allah says (interpretation of the meaning):
“(This is) a Book (the Qur’aan) which We have sent down to you, full of blessings, that they may ponder over its Verses, and that men of understanding may remember”
“Verily, this Qur’aan guides to that which is most just and right”
“Say: It is for those who believe, a guide and a healing”
End quote from Fataawa al-Shaykh Ibn Baaz, 11/364
And Allah knows best.