When comparing the two, both are about what? Not themselves, but about God.
There is an excellent reason for which the Divine Office (now known as Liturgy of the Hours or Christian Prayer) has its two most important prayer, the Morning and the Evening, include the Song of Zechariah and the Magnificat.
However, it would be gravely erroneous to compare the Forerunner with Our Lady. He was never “full of grace”, for as far as we know, when Our Lady visited her cousin Elizabeth (which explains just why she was chosen to be the mother of the Baptist) and Elizabeth heard her voice, her unborn child leaped of joy and *she *was filled with the presence of the Holy Spirit, meaning she received an extraordinary gift to acknowledge Our Lady as the Mother of God - indeed, the first human to do so.
John the Baptist was indeed the greatest among all prophets, for such was the word spoken by Christ, but was infinitely less that His mother. The Baptist himself was well aware of his humbleness before the Lord, for having received in mysterious ways divine knowledge of his mission as the Forerunner of the Christ, he endured a life of strict penance and mortification, and upon beginning his ministry, he openly manifested:
After me is coming someone who is more powerful than me, and I am not fit to kneel down and undo the strap of his sandals.
Our Lady, on the other hand, was found fit to give birth to Him, to be the true mother of the Christ.
Of her speaks the Sacred Scripture from Genesis to Revelation, of her speak the prophets and all the Church Fathers, and to her the Church looks as her image.
And much reflection is worth giving to the words of St. Paul:
the heavenly Jerusalem is the free woman, and she is our mother
He who has ears, let him hear.
For those who insist on negating the teachings of the Church for mysterious and erroneous reasons, especially for those who, following the trend of gravely erroneous doctrines, insist in asserting that any teaching successive to the Gospels is not worth of equal reverence, I remind the words of the Lord:
I have yet many things to say to you: but you cannot bear them now.
The Lord, head of the Church, speaks to Her through the guidance of the Holy Spirit. It is the Spirit, the same Spirit that came unto Mary, that filled Elizabeth, that confirmed and guided the Apostles, it is the very same Spirit that teaches us how greatly pleasing it is to the Father our prayers of thanksgiving, our prayers for the Poor Souls in Purgatory, our prayers through the intercession of the Church Triumphant, and above all else, our prayers through the intercession of Our Lady who is - great mystery - daughter of the Father, mother of the Son, spouse of the Spirit. Such great honor for a creature!
Indeed, kind Mother, the Lord has done great things for you, and all generations shall call you blessed, although not all will: for many throughout history have affirmed to love the Father, yet they have despised the Son, the Spirit, the Church, and you. The reasons that move them I ignore and cannot understand: for, having met people from each, I know they (or at least some of them) firmly believe that in such a gravely erroneous behavior they truly honor God. I am only sad that they, as the apostle wrote, see the light but fail to recognize it, whether it is shining through the Church, the saints, or you. They insist that they seek the light alone, yet they despise that which God has chosen as source of His light, that through which the Light came into the world and through which the Light chose to remain into the world.