"The mystery of the cross explains all other mysteries. In the light that streams from Calvary the attributes of God which had filled us with fear and awe appear beautiful and attractive. Mercy, tenderness, and parental love are seen to blend with holiness, justice, and power. While we behold the majesty of His throne, high and lifted up, we see His character in its gracious manifestations, and comprehend, as never before, the significance of that endearing title, “Our Father.” GC 652.1"
"For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life."
Both passages deal with God's love expressed through sacrifice and the resulting relationship with humanity. While John 3:16 is a foundational verse, the EGW passage expands on the implications of that love as revealed through the cross.
"It will be seen that He who is infinite in wisdom could devise no plan for our salvation except the sacrifice of His Son. The compensation for this sacrifice is the joy of peopling the earth with ransomed beings, holy, happy, and immortal. The result of the Saviour's conflict with the powers of darkness is joy to the redeemed, redounding to the glory of God throughout eternity. And such is the value of the soul that the Father is satisfied with the price paid; and Christ Himself, beholding the fruits of His great sacrifice, is satisfied. GC 652.2"
"He shall see of the travail of his soul, and shall be satisfied: by his knowledge shall my righteous servant justify many; for he shall bear their iniquities."
The EGW passage directly echoes the sentiment of Isaiah 53:11 regarding the satisfaction of Christ after his sacrifice. The phrase 'shall be satisfied' is a clear connection.