"About this time a terrible fire occurred in Rome by which nearly one half of the city was burned. Nero himself, it was rumored, had caused the flames to be kindled, but to avert suspicion he made a pretense of great generosity by assisting the homeless and destitute. He was, however, accused of the crime. The people were excited and enraged, and in order to clear himself, and also to rid the city of a class whom he feared and hated, Nero turned the accusation upon the Christians. His device succeeded, and thousands of the followers of Christ —men, women, and children—were cruelly put to death. AA 487.2"
"And ye shall be hated of all men for my name’s sake: but he that endureth to the end shall be saved."
Both passages describe the persecution and hatred faced by Christians. The EGW passage provides a specific historical example of the principle outlined in Matthew 10:22.
"From this terrible persecution Paul was spared, for soon after his release he had left Rome. This last interval of freedom he diligently improved in laboring among the churches. He sought to establish a firmer union between the Greek and the Eastern churches and to fortify the minds of the believers against the false doctrines that were creeping in to corrupt the faith. AA 487.3"
"I marvel that ye are so soon removed from him that called you into the grace of Christ unto another gospel: Which is not another; but there be some that trouble you, and would pervert the gospel of Christ. But though we, or an angel from heaven, preach any other gospel unto you than that which we have preached unto you, let him be accursed. As we said before, so say I now again, If any man preach any other gospel unto you than that ye have received, let him be accursed."
Both passages address the issue of false doctrines corrupting the faith. The EGW passage mentions Paul's efforts to fortify believers against false doctrines, while the Galatians passage warns against those who would pervert the gospel of Christ.
"But none of these things move me, neither count I my life dear unto myself, so that I might finish my course with joy, and the ministry, which I have received of the Lord Jesus, to testify the gospel of the grace of God."
Both passages highlight Paul's dedication to his ministry and his willingness to endure hardship for the sake of the gospel. The EGW passage speaks of Paul's labor among the churches, while the Acts verse speaks of finishing his course with joy and testifying to the gospel.