I have noticed in evangelical / Baptist circles that the phrase "your testimony" is mentioned heavily in suggestions as to how you ought to witness to nonbelievers. It is said that citing personal evidence of how God was active in your life, through miracles or improved moral behavior over time, is the trump card in your witness. I've also heard a Lutheran pastor say something like, "It is transformed, not perfect, lives that will witness to Christ." And I just now found similar "transformed, not perfect" wording on a Catholic site.
In contrast, the sermons I find most inspiring (and assume would be more convincing to a nonbeliever who was like myself) instead focus on a conviction of sin, and the futility of works, as a lead-in to Christ as Redeemer. For example, C.S. Lewis' Mere Christianity talks about the nature of God and our sin moreso than how he prayed and got something from God. A focus on material benefits and moral improvements risks missing out completely on the sin-death-resurrection narrative and are ultimately Antinomian.
Q: What are the theological roots of stressing "your testimony" in evangelism? (From bible to church fathers to contemporary great evangelists?)