"Not without hindrance was the Commander of heaven to win the souls of men to His kingdom. From the time when He was a babe in Bethlehem, He was continually assailed by the evil one. The image of God was manifest in Christ, and in the councils of Satan it was determined that He should be overcome. No human being had come into the world and escaped the power of the deceiver. The forces of the confederacy of evil were set upon His track to engage in warfare against Him, and if possible to prevail over Him. DA 116.1"
"And the dragon was wroth with the woman, and went to make war with the remnant of her seed, which keep the commandments of God, and have the testimony of Jesus Christ."
Both passages describe Satan's warfare against Jesus/the seed of the woman. The EGW passage focuses on Satan's attacks throughout Jesus' life, while Revelation 12:17 speaks of war against the remnant.
"At the Saviour's baptism, Satan was among the witnesses. He saw the Father's glory overshadowing His Son. He heard the voice of Jehovah testifying to the divinity of Jesus. Ever since Adam's sin, the human race had been cut off from direct communion with God; the intercourse between heaven and earth had been through Christ; but now that Jesus had come “in the likeness of sinful flesh” ( Romans 8:3 ), the Father Himself spoke. He had before communicated with humanity through Christ; now He communicated with humanity in Christ. Satan had hoped that God's abhorrence of evil would bring an eternal separation between heaven and earth. But now it was manifest that the connection between God and man had been restored. DA 116.2"
"For what the law could not do, in that it was weak through the flesh, God sending his own Son in the likeness of sinful flesh, and for sin, condemned sin in the flesh:"
Ellen White directly references Romans 8:3 in this passage.
"Satan saw that he must either conquer or be conquered. The issues of the conflict involved too much to be entrusted to his confederate angels. He must personally conduct the warfare. All the energies of apostasy were rallied against the Son of God. Christ was made the mark of every weapon of hell. DA 116.3"
"And I will put enmity between thee and the woman, and between thy seed and her seed; it shall bruise thy head, and thou shalt bruise his heel."
Both passages describe the conflict between Satan and Jesus. The EGW passage focuses on Satan's all-out effort to defeat Jesus, while Genesis 3:15 establishes the initial enmity and the eventual victory of the seed of the woman.