The difficulty for us is that there is a chapter division between 12:31 and 13:1, so we tend to think that 12:31 wraps up the discussion in chapter 12 and that chapter 13 begins a new topic. However, Paul did not write a big 13 in the middle of his letter, he wrote it as one continuous text. Therefore, I think it is wrong to try to figure out from 12:31 which of the previously listed gifts are greater.
If the church at Corinth were a modern church, we would call it a dysfunctional charismatic congregation. Paul says that any contest of ‘my gift is greater than your gift’ is improper. Without love, all these gifts are clanging gongs and clashing cymbals; noisy but not edifying. So instead of seeking after specific gifts to impress others with our spirituality (and what else could we be doing if we want to know whose gift is greater), we should seek first to love. We should love the people who are unworthy of our love, as Jesus did; we should love the people who hate us, as Zacchaeus did; we should love without hesitation, as Joseph of Arimathea did. We should love a self-sacrificing, burden-sharing love that lifts sinners into sainthood and that lifts saints into glory. For it seems to me that if we seek to love in that perfect way, any gift the Spirit gives us to accomplish that love is a ‘greater gift.’ Or perhaps all of the gifts in chapter 12 are lesser gifts, and the greater gifts come only through an earnest desire to love, and the greater gifts are not listed, because to one who loves, receiving gifts matters less than giving them.
I believe that in 12:31, Paul is looking forward, not backward. The greater gifts are faith, hope, and love; and the greatest gift is love.
Well, that’s just my crackpot opinion. All I know is that if you truly loved me as a friend, despite my many flaws, I would like that a lot more than if I heard you speak in tongues, prophesy the future, or teach me arcane doctrines. Without love, your tongues are noise, your prophecy is coincidence, your doctrines are interesting opinions. With love, they are all transformed… and so am I.