Which is better -- reading Quran or listening to it on tapes?

Praise be to Allah.

Reading Quran 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 Quran from other people. 

Al-Bukhaari (4582 and 5049) and Muslim (800) narrated from ‘Abd-Allah ibn Mas’ood (may Allah be pleased with him) that he said: The Messenger of Allah (blessings and peace of Allah upon him) said to me: “Recite the Quran to me.” I said: O Messenger of Allah, 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 ) 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 Quran) which We have sent down to you, full of blessings, that they may ponder over its Verses, and that men of understanding may remember” [Saad 38:29]

“Verily, this Quran guides to that which is most just and right” [al-Isra’ 17:9]

“Say: It is for those who believe, a guide and a healing” [Fussilat 41:44]. 

End quote from Fatawa al-Shaykh Ibn Baz, 11/364 

And Allah knows best.