In the Catholic view of evangelism, what is it that we are trying to accomplish in the potential convert? Our protestant brethren are most often trying to change the person's view of Christ; which is a noble effort, and is sometimes accomplished. The problem with this is that in seeking to change just one aspect of a person's point of view, we leave the rest to chance. What will a person think about the sacraments? What will they think about the Church? What will they think about holiness? If we do not fill those issues with a certain content, then there are many directions that a person can go in theologically.
This is to say, that we are aiming at changing a person's entire view of the world, not just their view of who can save them from their problems. To aim at making the person see Who is the Savior of the world is certainly a good thing, but it is not sufficient; especially in modern society when the very concept of "savior" is so unclear. Furthermore, if we limit ourselves to the salvation aspect of our Lord Christ, then we have the great potential of encouraging conversions based solely on selfish motives. Guilty feelings about one's sin are never a sufficient basis for forgiveness or reason for conversion (cf. CCC 1453).
Catholic evangelism is not merely attempting to "convince" someone of a certain fact, it is aiming rather at explaining a body of facts and then encouraging that person to respond rightly to this "new world" that he has found himself in. That may seem like merely a matter of the quantity of doctrinal content; it is much more. One or two facts removed from the larger whole are often open to varying interpretations (that is why protestants who all use the same basic method of evangelism still are split into a multitude of denominations). When we lay out for a person an entire world view--most specifically the view of a world that Jesus is redeeming through the ministry of His Church--that person cannot remain neutral, he must act on that new reality.
In essence, the protestant view of evangelism is . . . well . . . very protestant. It is based in an individualistic perspective that unintentionally (I hope) leads the convert to a very prideful and selfish manner of life; the attempt to meld this selfishness with Christian ethics is what often causes fights in protestant circles (I have seen many of them first-hand). It is difficult--not impossible, but difficult--to encourage the virtues of faith, hope and love, and a life of self-sacrifice, when the spiritual life was begun on selfish grounds. To maintain the same view of the world and only add in a new character of Jesus as Savior does not lead anyone to full submission to God; much more must happen if we are to grow in faith and not stagnate in individualistic self-service.
In Scripture (both Old and New Testaments) faith is not something that ever happens to us privately. It is always in relation to the larger body of God's people and to society around. The gospel Jesus told the Apostles to preach was never something that was only going to "save the soul"; it was something that was going to transform society, and that is what every baptized person is called to be a part of. Even our protestant brethren recognize this (it "spills over" from the grace of their baptism) but they have to try to figure out how to fulfill this calling without the Tradition of the Church to guide them (which usually leads to grave divisions). If we evangelize outside of the larger context of all that it entails, then are we truly doing evangelism?
Knowing the full extent of the gospel means that we will need to confront more than the sinful individual with the Lordship of Christ. It means that we will also have to confront the entire world around. The Catholic Church has never been much for bowing to civil authorities, and (usually) tries to avoid being led by the fashions of the world and the ideas of the devil. Countless Saints have shed their blood in order to say "No" to the world's view of things. They knew that submission to Christ involved their whole life, and that is what evangelism should be aiming at: bringing people to the point where they will give their whole life to Christ.