In the Constitution on the Sacred Liturgy from Vatican Council II it says that “every liturgical celebration (which would include the LOTH) because it is an action of Christ the Priest and of his Body, which is the Church, is a sacred action surpassing all others. No other action of the Church can equal its efficacy by the same title and to the same degree”. So the LOTH is a wonderful and powerful prayer and it is recommended to the laity by the church.
The rosary of Our Lady is also a wonderful and powerful prayer. Many popes and saints have recommended it to the faithful. St Louis Marie de Montfort wrote a wonderful work on the rosary titled The Secret of the Rosary. Pope John Paul II wrote an Apostolic Letter, ROSARIUM VIRGINIS MARIAE, on the rosary and had proclaimed 2002-2003 the Year of the Rosary. He also said the rosary was his favorite prayer. Pope Leo XIII is called the pope of the rosary. Our Lady herself told the children of Fatima to pray the rosary daily.
In ROSARIUM VIRGINIS MARIAE, Pope John Paul II wrote: “There are some who think that the centrality of the Liturgy, rightly stressed by the Second Vatican Ecumenical Council, necessarily entails giving lesser importance to the Rosary. Yet, as Pope Paul VI made clear, not only does this prayer not conflict with the Liturgy, it sustains it, since it serves as an excellent introduction and a faithful echo of the Liturgy, enabling people to participate fully and interiorly in it and to reap its fruits in their daily lives”.
Now most lay people are not required to recite either the LOTH or the rosary. So which should you choose? I would choose that which my heart felt inclined too, the one that I think I would do regularly. Though you might feel inclined to recite the other one sometime in the future or maybe both.
I have prayed both the LOTH and the rosary. However, presently I’m only praying the rosary daily. I can pray the rosary anytime and anywhere which fits in very nicely with my daily schedule. I’m also very attracted to the rosary, I love to pray it and I love our Lady.