What really affects our salvation is not different versions of the Bible, but whether we see ourselves as sinners who have broken most of the Ten Commandments, and outside of Christ, will come up to judgment and be found guilty and be sentenced to God's eternal prison without parole. Unless the unsaved person sees that clearly, the gospel will not be good news for him, and he will not understand exactly why Jesus came and died on the cross. If they don't see themselves as sinners, but as good people all they will do is to adopt the Christian religion to enhance the life in this world, and as soon as suffering, sickness, and persecution comes along, they will give it all up and fall away.
It is a fact that most evangelistic efforts achieve less than 5% of those making decisions for Christ actually end up in fellowship. This was shown in an evangelistic crusade, 280,000 people made decisions for Christ, but it was found that only 14,000 of them were discovered fellowshiping as members of Christian churches. The rest had gone back into the world. That meant a 5% success rate for all the time and effort that was made to get the decisions. This is the same for most evangelistic crusades, including those conducted by Billy Graham.
This is because the gospel presented is that God has a great plan for our lives, and He loves us and if we invite Jesus into our hearts, life will be happy and meaningful and we will go to heaven. But when life fails to give that happiness and meaning, most will be disillusioned, felt that they were lied to, and reject Christ and the church as a result, and it will be almost impossible for anyone else to successfully witness the gospel to them in the future.
So, in fact, it is the type of gospel that is being present is what is turning people to atheism after they have originally believed it and made a decision for Christ.
The most successful converts for Christ have been those who were presented with their sinful life as compared to the Ten Commandments, and the expectation of judgment and hell when they die. Then the gospel that shows that Jesus came and took the penalty for their sin is really good news for them, and they see the need to repent and turn from their sinful lifestyle. And, even though life turns to custard for them later, their foundation is in Christ and what He has done on the cross for them, and so they are prepared to endure the suffering and persecution that comes with the territory of being a Christian believer.
So, it has nothing significant to do with different versions of the Bible, but the version of the gospel that is being shared with them.