When we think of the various spiritualities in the Church we can easily compare them on a superficial level of structure, of founders or of nationalities. I think one of the easiest is to explain the differences by the primary underlying experience of God in each one. Obviously, such a description is not going to be extensive, but it sheds light on the variations throughout that spirituality. I admit I may not have a perfect grasp of each spirituality mentioned, but I hope these help.
Carmelites: Configuration with the crucified Christ
Opus Dei: The experience of God as Father – we are beloved children of God
Jesuits: The emptiness of the world and the fullness in Christ – the meditation of the two ways: Christ or the world
Missionaries of Charity: Christ present in the poor and suffering – whatsoever you do to the least of my brothers, that you did unto me: a daily living of Matthew 25
Charismatic renewal: The experience of the Holy Spirit active in our lives today
Dominicans: Christ present in the community – or as one Dominican put it: we are about corporate holiness, you are only as holy as your community
Franciscans: The poverty, humility and simplicity of Bethlehem and Nazareth – go, sell what you have and follow me
Regnum Christi and the Legion: The call of Christ to be an Apostle – Christ’s charity urges us on
Even if Regnum Christi became a personal prelature tomorrow it would not be Opus Dei, a Christ-centered and Father-centered spirituality have a difference at the root. Hopefully this difference at the base helps you understand the more visible differences.