Your question can be taken two ways: What is the difference between the parishes, or what is the difference between the priests themselves? I’ll start with the parishes. Any full-blown parish is part of the diocese in which it is located and is therefore diocesan, regardless of who staffs it. (Some religious orders have public chapels that are not technically parishes and they are a different matter.) Even if the religious order owns the parish property, canonically, the parish remains under the auspices of the local bishop. A special gift religious priests bring to parish ministry is their own unique charism, and so a visitor might notice a difference between a parish staffed by Franciscans, Dominicans or Jesuits. Diocesan priests usually come from among the people they serve and that, too, is a unique charism.
As far as the difference between diocesan and religious priests, we sometimes over-emphasize it. I was a religious priest for 11 years before transferring to the Archdiocese of St. Louis, and I’ve found that diocesan and order priests have more in common than not. There is one priesthood of Jesus Christ, and both categories of priests share in it. We all celebrate Mass and pray the Liturgy of the Hours daily, and, if we are in a parish, whether we are religious or diocesan, we carry out the same basic ministry. We both strive daily to configure our lives to Christ and minister in His name. Finally, we are encouraged to live and pray together and maintain a deep sense of unity, although for religious, this is an indispensable aspect of communal life.
There are important differences as well. Diocesan priests are ordained to minister to the people of God in a specific diocese, whereas religious priests minister wherever their superiors assign them. In regard to religious priests, there are many different types of orders, each one shaped by the charism of their founder. (For example, ordained monks live in a close-knit monastic community, missionary priests carry the Gospel to foreign lands, etc.) While both religious and diocesan priests commit to celibacy and obedience, religious do so by vow whereas diocesan priests do so by promises made to their bishop. Both are expected to maintain simplicity of life; religious renounce personal ownership through a vow of poverty, and diocesan priests retain ownership of their possessions while practicing generous stewardship.
So which type of priest is holier? Having worked both sides of the street, I can say neither. The only thing that matters is that we are faithful to the vocation God has given us. If we surrender our lives completely to Christ and seek to do His will in all things, then God will help us to become holy, whatever our vocation. That is as true for religious and diocesan priests as it is for any other baptized Christian.
Father Scott Jones is pastor of Sts. Teresa and Bridget Parish in St. Louis.