Yes, there does appear to be "greater gifts":
But earnestly desire the greater gifts. And I show you a still more excellent way. 1 Corinthians 12:31 NASB
Pursue love, yet desire earnestly spiritual gifts, but especially that you may prophesy. For one who speaks in a tongue does not speak to men but to God; for no one understands, but in his spirit he speaks mysteries. 3 But one who prophesies speaks to men for edification and exhortation and consolation. 4 One who speaks in a tongue edifies himself; but one who prophesies edifies the church. 5 Now I wish that you all spoke in tongues, but even more that you would prophesy; and greater is one who prophesies than one who speaks in tongues, unless he interprets, so that the church may receive edifying. 1 Corinthians 14:1 NASB
Paul here emphasizes that prophecy edifies the church and places it as a superior gift than tongues--at least when tongues are not interpreted. Paul expounds on this throughout chapter 14.
But now, brethren, if I come to you speaking in tongues, what will I profit you unless I speak to you either by way of revelation or of knowledge or of prophecy or of teaching? 7 Yet even lifeless things, either flute or harp, in producing a sound, if they do not produce a distinction in the tones, how will it be known what is played on the flute or on the harp? 8 For if the bugle produces an indistinct sound, who will prepare himself for battle? 9 So also you, unless you utter by the tongue speech that is clear, how will it be known what is spoken? For you will be speaking into the air. 10 There are, perhaps, a great many kinds of languages in the world, and no kind is without meaning. 11 If then I do not know the meaning of the language, I will be to the one who speaks a barbarian, and the one who speaks will be a barbarian to me. 12 So also you, since you are zealous of spiritual gifts, seek to abound for the edification of the church.
13 Therefore let one who speaks in a tongue pray that he may interpret. 14 For if I pray in a tongue, my spirit prays, but my mind is unfruitful. 15 What is the outcome then? I will pray with the spirit and I will pray with the mind also; I will sing with the spirit and I will sing with the mind also. 16 Otherwise if you bless in the spirit only, how will the one who fills the place of the ungifted say the “Amen” at your giving of thanks, since he does not know what you are saying? 17 For you are giving thanks well enough, but the other person is not edified. 18 I thank God, I speak in tongues more than you all; 19 however, in the church I desire to speak five words with my mind so that I may instruct others also, rather than ten thousand words in a tongue. 1 Corinthians 14:6-19 NASB