Mantras, and the rosary are a mechanical way to quiet distractions. But so is quietly sitting with a Bible in front of you, reading and pondering a verse or a story, letting the words into our heart. FOr that matter, pumping iron, jogging, or knitting lets us quiet distractions to get into our inner selves. (I frequently play piano for this).
The state of quiet is good for the body, since it quiets stress.
Spiritually, however, these things are a world apart. If one merely says "mantras" or "the rosary (i.e. words only)" or rushes through bible verses, they are merely words. They relax, but we only find ourselves. We may as well knit, for then we'd have an afghan afterward. There is a danger that pure "relaxation" leads only to egotism/pride.
However, if we are searching for the Lord in our hearts, being quiet in the presence of God and listening to his word will be the aim. So we can pray the rosary, or knit, or cook and find his presence.(see Brother Lawrence book practicing the presence of God).