"The question that Christ put to Peter was significant. He mentioned only one condition of discipleship and service. “Lovest thou Me?” He said. This is the essential qualification. Though Peter might possess every other, without the love of Christ he could not be a faithful shepherd over the Lord's flock. Knowledge, benevolence, eloquence, gratitude, and zeal are all aids in the good work; but without the love of Jesus in the heart, the work of the Christian minister will prove a failure. GW 183.1"
"So when they had dined, Jesus saith to Simon Peter, Simon, son of Jonas, lovest thou me more than these? He saith unto him, Yea, Lord; thou knowest that I love thee. He saith unto him, Feed my lambs. He saith to him again the second time, Simon, son of Jonas, lovest thou me? He saith unto him, Yea, Lord; thou knowest that I love thee. He saith unto him, Feed my sheep. He saith unto him the third time, Simon, son of Jonas, lovest thou me? Peter was grieved because he said unto him the third time, Lovest thou me? And he said unto him, Lord, thou knowest all things; thou knowest that I love thee. Jesus saith unto him, Feed my sheep."
The EGW passage directly references and interprets the conversation between Jesus and Peter in John 21:15-17. The phrase "Lovest thou Me?" is a direct quote, and the passage focuses on the importance of love for Christ in ministry, which is the central theme of the biblical passage.
"And though I have the gift of prophecy, and understand all mysteries, and all knowledge; and though I have all faith, so that I could remove mountains, and have not charity, I am nothing."
Both passages emphasize that certain qualities or gifts are worthless without love/charity. EGW states that knowledge, benevolence, etc., are useless without the love of Jesus, while 1 Corinthians 13:2 states that prophecy, understanding, knowledge, and faith are nothing without charity.
"Feed the flock of God which is among you, taking the oversight thereof, not by constraint, but willingly; not for filthy lucre, but of a ready mind;"
Both passages relate to the idea of shepherding or feeding the flock of God. EGW connects the question "Lovest thou Me?" to being a faithful shepherd, while 1 Peter 5:2 directly instructs elders to "Feed the flock of God." Although not a direct quote, the thematic connection is strong.
"“The elders which are among you I exhort, who am also an elder, and a witness of the sufferings of Christ, and also a partaker of the glory that shall be revealed: Feed the flock of God which is among you, taking the oversight thereof, not by constraint, but willingly; not for filthy lucre, but of a ready mind; neither as being lords over God's heritage, but being ensamples to the flock. And when the Chief Shepherd shall appear, ye shall receive a crown of glory that fadeth not away.” [ 1 Peter 5:1-4 .] GW 183.3"
"The elders which are among you I exhort, who am also an elder, and a witness of the sufferings of Christ, and also a partaker of the glory that shall be revealed: Feed the flock of God which is among you, taking the oversight thereof, not by constraint, but willingly; not for filthy lucre, but of a ready mind; Neither as being lords over God’s heritage, but being ensamples to the flock. And when the chief Shepherd shall appear, ye shall receive a crown of glory that fadeth not away."
Ellen White directly references 1 Peter 5:1-4 in this passage.