I've recently completed reading The Open Secret: An Introduction to the Theology of Mission by Lesslie Newbigin. In this text Newbigin presents more than just a theology of mission, but a framework for understanding the history of Christian mission as well as core values for understanding the mission of the church.
In Chapter 9 he shares an outline of Margaret Kane's contrasting views of the church's mission from her book Theology in an Industrial Society. The table asserts two differing views on the church's mission, as though through the eyes of church A and church B. Here's the table:
Church A: God is known through unchanging propositions, handed on from the past in large abstract concepts -- sin, judgment, repentance, redemption, etc.
Church B: God is known by personal meeting in and through persons and events in the present.
Church A: Theology is a study of the Bible and what people have made of it, and is to be done by academic experts.
Church B: Theology is a continuing process of interpreting contemporary experiences in light of God's revelation in Christ, and is to be done by everyone.
Church A: The church consists of those called out of an evil world. It's task is to obey the command to preach the gospel and to save souls out of the world. To do this it must build up its own organization in a disciplined way. Clergy lead and laypeople must help them.
Church B: Sharp distintions between those who do or do not belong to church are not helpful. The church's job is to penetrate the world and point to the signs of God's activity in it. The whole creation is to be redeemed. And laypeople have a crucial ministry in the world and clergy must help them.
Church A: The soul is the important part of a human, and humans must beware of the body and materialism. A human is an isolated individual.
Church B: A human is a total person, body and spirit. A human's life has meaning only in relation to his or her total social and historical context.
Church A: Divinity is stressed.
Church B: Humanity is stressed.
Kane does not assert that all church's are either completely church A or completely church B. Nor does she completely endorse one over the other. Most churches are likely a little bit of both but with tendencies in one direction or the other. However, Kane does assert that the values of church B are becoming more and more neccessary for churches to have a participation in mission with any relevance to contemporary society.
I found this table helpful for understanding why different types of churches undertake mission differently. Obviously, if the held set of values is different the acting out of those values will naturally be different.