"Chapter 9—John in Exile The wonderful success which attended the preaching of the gospel by the apostles and their fellow laborers increased the hatred of the enemies of Christ. They made every effort to hinder its progress, and finally succeeded in enlisting the power of the Roman emperor against the Christians. A terrible persecution ensued, in which many of the followers of Christ were put to death. The apostle John was now an aged man, but with great zeal and success he continued to preach the doctrine of Christ. He had a testimony of power, which his adversaries could not controvert, and which greatly encouraged his brethren. SL 70"
"I John, who also am your brother, and companion in tribulation, and in the kingdom and patience of Jesus Christ, was in the isle that is called Patmos, for the word of God, and for the testimony of Jesus Christ."
Both passages refer to John's experience during a time of persecution. Revelation 1:9 mentions John's exile on Patmos, and the EGW passage discusses John's exile and the persecution of Christians. While not a direct quote, the EGW passage provides context and elaboration on the situation mentioned in Revelation 1:9.
"When the faith of the Christians would seem to waver under the fierce opposition they were forced to meet, the apostle would repeat, with great dignity, power, and eloquence, “That which was from the beginning, which we have heard, which we have seen with our eyes, which we have looked upon, and our hands have handled, of the Word of life; ...that which we have seen and heard declare we unto you, that ye also may have fellowship with us: and truly our fellowship is with the Father, and with his Son Jesus Christ” ( 1 John 1:1-3 ). SL 70.2"
"That which was from the beginning, which we have heard, which we have seen with our eyes, which we have looked upon, and our hands have handled, of the Word of life;"
EGW directly quotes 1 John 1:1-3.
"That which was from the beginning, which we have heard, which we have seen with our eyes, which we have looked upon, and our hands have handled, of the Word of life; (For the life was manifested, and we have seen it, and bear witness, and shew unto you that eternal life, which was with the Father, and was manifested unto us;) That which we have seen and heard declare we unto you, that ye also may have fellowship with us: and truly our fellowship is with the Father, and with his Son Jesus Christ."
Ellen White directly references 1 John 1:1-3 in this passage.
"The bitterest hatred was kindled against John for his unwavering fidelity to the cause of Christ. He was the last survivor of the disciples who are intimately connected with Jesus, and his enemies decided that his testimony must be silenced. If this could be accomplished, they thought the doctrine of Christ would not spread; and if treated with severity, it might soon die out of the world. John was accordingly summoned to Rome to be tried for his faith. His doctrines were misstated. False witnesses accused him as a seditious person, publicly teaching theories which would subvert the nation. SL 70.3"
"If the world hate you, ye know that it hated me before it hated you."
Both passages deal with the hatred directed towards followers of Christ. The EGW passage describes the hatred towards John, while the Bible verse speaks generally about the world's hatred for Christ's followers. The connection is valid and meaningful.
"Now about that time Herod the king stretched forth his hands to vex certain of the church. And he killed James the brother of John with the sword. And because he saw it pleased the Jews, he proceeded further to take Peter also. (Then were the days of unleavened bread.) And when he had apprehended him, he put him in prison, and delivered him to four quaternions of soldiers to keep him; intending after Easter to bring him forth to the people. Peter therefore was kept in prison: but prayer was made without ceasing of the church unto God for him."
Both passages describe the persecution of early Christians. The EGW passage focuses on John, while the Bible verse describes the persecution of James and Peter. The connection is valid, though not a direct parallel.