in all of our training, we emphasized that we wanted the people we met to encounter something of God's Kingdom 1st, before we spoke to them the Gospel verbally. Whereas BOTH approaches are Biblical (sometimes Jesus preached 1st, and then demonstrated miraculously and other times the demonstration came 1st), I believe that in America we find ourselves needing to demonstrate the Kingdom supernaturally BEFORE we try to talk about Christ.
This happened on the streets on Saturday over and over again. An accurate word of knowledge, a physical healing, meaningful prophetic ministry or even an encounter with God's love. I am reminded of one Arab muslim man who witnessed the healing of a friend of his AND THEN I was able to speak boldly about the Jesus who just came in a miraculous demonstration. He gladly took the Arabic New Testament I offered him and I spoke about Christ's Deity openly (which isn't always easy with muslims). He told me he would cherish the gift I came him (the NT) and would study it carefully. I know that without the demonstration of a healing miracle, I would have never been able to speak as clearly about Christ without an argument. No debates, no arguments about muhammad and the quran - Jesus was all we talked about!
All afternoon, Kingdom encounters came 1st and then we spoke more about the Gospel message. I heard from other teams and heard exactly the same types of stories. Several people gave their lives to Christ.
I believe we have a serious credibility problem in minds of many unbelievers and yet, when the Kingdom comes in power, our credibility is often instantly restored and they are asking us about the Jesus who just healed them.