Short Answer: there isn't a contradiction

A reference to the larger treatment of both Prayer and the Eucharist in the Catechism, and not taking out of context the official teaching should prevent seeing a contradiction in what the Pope said (which conformed to the agenda of the 2005 Ordinary Synod).

Amplification

The answer is within the brief quote from the Pope (per @AndrewLeach's entry that you linked to) if we look at the whole quote.

The Eucharistic Celebration is the greatest and highest act of prayer, and constitutes the centre and the source from which even the other forms receive "nourishment": the Liturgy of the Hours, Eucharistic adoration, Lectio divina, the Holy Rosary, meditation. All these expressions of prayer, which have their centre in the Eucharist, fulfil the words of Jesus in the priest's day and in all his life: "I am the good shepherd; I know my own and my own know me, as the Father knows me and I know the Father; and I lay down my life for the sheep" (Jn 10: 14-15).

For starters: the Church teaches through the Catechism (1324) that

1324 The Eucharist is "the source and summit of the Christian life."

The Catechism as a whole addresses all elements of Christian life, as the Church sees them. This includes prayer: all of Section IV of the Catechism covers Prayer. Prayer in general is thus a subset of the larger thing, Christian life, as addressed in all 2865 articles.

The "apparent" contradiction looks like taking things out of context. I've fallen into the context problem myself more than once.

• It is worth noting that the context of the Pope's remarks is an address to clergy, who have a further obligation for more and daily prayer than the laity.

  There isn't a competition between the Eucharist and the Our Father, nor does the Pope's message and commentary imply that, nor will you find an "in church" source that agrees that there is a conflict.

The two are in harmony. (See Catechism 2770-2772 below). This is ably demonstrated during the Mass, since one of the prayers included is the Our Father, during the Liturgy of the Eucharist (cf Roman Missal, 3d edition).

In describing the Eucharist as a prayer (per the Pope's citation) rather than as a rite or a celebration of thanksgiving, Pope Benedict names it both an act of prayer and then discusses other forms of prayer. His meaning (in context) is that the Eucharist is also a a form of prayer. (Usually, a great collective prayer).

The authority of a Pope: his utterances, encyclicals, and commentaries can be authoritative without having to be ex cathedra. He is the Head of the Church, and the Head of the Magisterium of the Church, which is the church's ultimate teaching authority. That this quote is in accord with a previous proceeding of the Synod argues that there isn't a conflict.

The Our Father as the Perfect Prayer? Sure it is. Why wouldn't it be?

It was passed down from Jesus to his Disciples, so you can (from the Trinity perspective) say that God(The Son) gave this prayer to His People/The Faithful -- since He is perfect, the prayer is perfect.

From the Catechism

2765 The traditional expression "the Lord's Prayer" - oratio Dominica - means that the prayer to our Father is taught and given to us by the Lord Jesus. The prayer that comes to us from Jesus is truly unique: it is "of the Lord." On the one hand, in the words of this prayer the only Son gives us the words the Father gave him: he is the master of our prayer. On the other, as Word incarnate, he knows in his human heart the needs of his human brothers and sisters and reveals them to us: he is the model of our prayer.

The harmony is confirmed in the Eucharistic celebration itself.

124. After the chalice and paten have been set down, the Priest, with hands joined, says:
     At the Savior’s command and formed by divine teaching, we dare to say:
     He extends his hands and, together with the people, continues:

And everyone says the Our Father. (Ref = Liturgy of the Eucharist, Roman Missal, 3rd edition)

Bottom line:

• There isn't a conflict
• There are multiple forms of prayer.
• When the Eucharist is seen as a prayer, it is consistent with the position of the Eucharist in the Faith (source and summit of the faith) that it is the highest form of prayer, or as the Pope said it, the highest act of prayer.
• The Pope has sufficient authority to make such an observation as amplification of the teachings in the Catechism.
• That the Eucharistic celebration includes the Our Father looks like a strengthening of that statement: the highest act of prayer should include "the perfect prayer" within it.

2770 In the Eucharistic liturgy the Lord's Prayer appears as the prayer of the whole Church and there reveals its full meaning and efficacy. Placed between the anaphora (the Eucharistic prayer) and the communion, the Lord's Prayer sums up on the one hand all the petitions and intercessions expressed in the movement of the epiclesis and, on the other, knocks at the door of the Banquet of the kingdom which sacramental communion anticipates.

2771 In the Eucharist, the Lord's Prayer also reveals the eschatological character of its petitions. It is the proper prayer of "the end-time," the time of salvation that began with the outpouring of the Holy Spirit and will be fulfilled with the Lord's return. The petitions addressed to our Father, as distinct from the prayers of the old covenant, rely on the mystery of salvation already accomplished, once for all, in Christ crucified and risen.

2772 From this unshakeable faith springs forth the hope that sustains each of the seven petitions, which express the groanings of the present age, this time of patience and expectation during which "it does not yet appear what we shall be." The Eucharist and the Lord's Prayer look eagerly for the Lord's return, "until he comes."