A quick aside here - In any discussion involving change there is often a tendancy to disparage the new and defend the old or to disregard the old and embrace the new. It is important to recognize that people do not deliberately choose to be 'mistaken' - we come to the positions we hold with the best intentions, making the best use we can of the information and understanding at our disposal, within the context of our time and place. It is incumbant upon us to respect and honor those who have long ago gone before us as well as those with whom we differ today - probably a topic to address more fully at another time.
Back to the APC/MRI comparison, keeping in mind that the APC model grew out of a time when the church had a different place in mainstream culture than it does today.
APC ------------- vs ---------- MRI
Attractional ----vs--- Missional
Propositional --vs--- Relational
Colonial --vs--- Incarnational
Attractional - fundamental focus is getting people to come to and stay with the church. Programs and decisions are implemented in an attempt to satisfy people's needs and preferences - whether children's programs, worship styles, color of the paint in the auditorium - the focus is on what will get, and retain, people into the church building.
Propositional - fundamental focus is on being right or correct. Not a recent phenomenon - the pharisees were a prime example - there is the belief that there is a correct position or answer that can logically or rationally be found for any issue, and the goal is to convince ourselves and others that our position is the correct one.
Colonial - fundamental focus is on reproducing the pattern that is attractionally successful and propositionally correct. A franchise model - the McDonald's philosophy - the goal is to reproduce clones or semi-clones that are modeled after the right pattern.
This model is very much a part of my heritage and still very prevalent today. It is a heritage that I value and I love those who are a part of it, but I believe that the model is one that will not work in the context of a postmodern, post christendom world. Sweet says that the model that more nearly reflects the model in Acts, and that has a chance of reaching people in today's world is...
Missional - the focus is on going out - among the community, among the people, among the world - and 'as you are going make disciples'; there is an attractional aspect, but the attraction is to Jesus, not to the church and its building, programs, etc. The mission statement is the great commission.
Relational - the focus is on bringing people into relationship with God by building relationships rather than by convincing them of the correctness of our doctrine. There is a focus on learning to love our neighbor rather than being able to debate them.
Incarnational - the focus is on living in a way that reflects Jesus, on becoming the gospel, to be good news to a lost world. There is an emphasis on living among people and treating them as Jesus did those he lived among, addressing the needs that Jesus was concerned with.