"Christ promised that the Holy Spirit should abide with those who wrestle for victory over sin, to demonstrate the power of divine might by endowing the human agent with supernatural strength and instructing the ignorant in the mysteries of the kingdom of God. Of what avail would it be to us that the only begotten Son of God humbled Himself, endured the temptations of the wily foe, and died, the just for the unjust, if the Spirit had not been given as a constant, working, regenerating agent, to make effectual in each individual case what has been wrought out by the world's Redeemer? GW 286.1"
"Howbeit when he, the Spirit of truth, is come, he will guide you into all truth: for he shall not speak of himself; but whatsoever he shall hear, that shall he speak: and he will shew you things to come."
The EGW passage directly discusses the role of the Holy Spirit in guiding believers and empowering them, which aligns with John 16:13. The EGW passage amplifies the role of the Holy Spirit as the 'Spirit of truth' mentioned in John.
"work, seeking to draw the attention of men to the great sacrifice made upon the cross of Calvary, to unfold to the world the love of God to man, and to open to the convicted soul the promises of the Scriptures. GW 286.2"
"And when he is come, he will reprove the world of sin, and of righteousness, and of judgment:"
Both passages discuss the work of the Holy Spirit. John 16:8 speaks of the Spirit reproving the world of sin, righteousness, and judgment, while the EGW passage speaks of the Spirit drawing attention to the sacrifice of Christ and unfolding God's love. These are related aspects of the Spirit's work.