Impetinens has captured many of the differences. As a Franciscan myself, I’d like to clarify some points.
Let’s talk about priesthood. The priesthood is not essential to the religious life. The religious life is a complete way of life by itself. The priesthood is not more essential to the religious life than it is to the married life. Religious need priests for the same reasons that lay people who are married need them, the sacraments. That being said, there are religious orders and religious congregations (not the same thing) that were founded specifically to perform priestly ministries. The Order of Preachers (Dominicans) is one of them. They were founded to be preachers in the formal sense (deacons and priests).
The Friars Minor (Franciscans) were never founded. We happened by accident. Francis set out to live his life according to the Beatitudes. Others took notice of him and followed him. Among them there were priests, scholars, merchants, farmers, noblemen and men from many walks of life. That’s why we still call ourselves Friar, which is really very bad English for the Latin word, Frater or Brother. As these men came together, they formed a brotherhood. Later, women joined them and later, married couples and diocesan priests joined them. Eventually, Francis organized his family into three distinct orders: Friars, Nuns and everyone else: seculars, more friars and religious sisters. They are often referred to as the 1st, 2nd and 3rd orders, because of the chronology, not rank.
Those brothers who are priests often perform priestly work, some do not. We have brother-priests who run soup kitchens, serve as maintenance men, are teachers, serve as spiritual directors, or are administrators. In other words, all of our brothers go where ever there is a need. Our ordained brothers (priests) have no special place in the community nor do they have special rights, because they are ordained.
In this, the Dominicans are similar. Their ordained brothers do not have a special place or special rights in their order either, except for one. The Prior must be ordained. They have friars who are not ordained who are very involved in the ministry. However, they do consider the vocation to be a Dominican brother and the vocation to be a Dominican priest to be two different, but complimentary vocations.
Among Franciscans, there are no two different vocations. Everyone enters for one reason, to be a son or daughter of St. Francis. Therefore, a friar (ordained or not), a nun, a sister, a Secular Franciscan are all equal. Each has a ministry according to his gifts and according to the rule of the order.
Now let’s talk about poverty. There is a slight difference between the two orders and there is a similarity. Dominic and Francis insisted that their friars not own property. Both make solemn vows of poverty. However, the Dominicans (men and women) may own property in common or what we would call corporate property. Therefore, they live in houses called Priories.
Franciscans may not own property in common or individually. Therefore, any property that the Franciscans “own” (notice the quotation marks), is really Church property. When the time comes to leave it, the friars may not profit from it. It must be surrendered to the Church. It does not belong to the friars, even though the friars raised the funds. The same applies to the nuns, sisters and Secular Franciscans. Joint property must be surrendered to the Church when no longer useful or when the Church demands it. This is not the case with the Dominicans. It is their property to do with as they wish. But no individual may claim to any of it.
Let’s talk about ministry. The primary ministry of the Dominican family is to preach. Hence they are the Order of Preachers. The primary ministry of Franciscans is to live the Gospel in fraternity. When a Dominican goes out, he goes out to preach. When a Franciscan goes out, he goes out as a brother among many. He preaches by word and life. This takes us back to poverty. How does he live his life and where? He lives his life among the most sinful, the poorest, the immigrant, the unwanted, the unconverted, but most especially among the unconverted Catholic.
The Dominicans were founded to go out and fight heresy. Francis attempted to be a missionary to the Muslims, but that did not work out. When he returned, Clare pointed out to him that Catholics where worse Christians than Muslims were. He made it his mission to convert Catholics back to the Church. Thus, he wrote a number of letters and admonitions for Catholics. That’s how the Secular Order came to be founded. It was a way of bringing Catholic laymen and women into the religious life. It was the first secular order in the history of the Church and it is the only Secular Order that is canonically erected as an independent order of Pontifical Right with its own government, rule, constitutions and papal delegate. All the other Lay Orders and Secular Orders are associations dependant on the religious. Not so with the Secular Franciscans. In this sense, the Franciscan family is much more independent than the Dominicans are. Each order has its own government, its mission and its canonical place in the Church.