"Abiding peace, true rest of spirit, has but one Source. It was of this that Christ spoke when He said, “Come unto Me, all ye that labor and are heavy-laden, and I will give you rest.” Matthew 11:28 . “Peace I leave with you, My peace I give unto you: not as the world giveth, give I unto you.” John 14:27 . This peace is not something that He gives apart from Himself. It is in Christ, and we can receive it only by receiving Him. MH 247.1 Christ is the wellspring of life. That which many need is to have a clearer knowledge of Him; they need to be patiently and kindly, yet earnestly, taught how the whole being may be thrown open to the healing agencies of heaven. When the sunlight of God's love illuminates the darkened chambers of the soul, restless weariness and dissatisfaction will cease, and satisfying joys will give vigor to the mind and health and energy to the body. MH 247.2"
"Peace I leave with you, my peace I give unto you: not as the world giveth, give I unto you. Let not your heart be troubled, neither let it be afraid."
The EGW passage directly quotes John 14:27 and Matthew 11:28, making it an explicit allusion. The surrounding text further explains and expands on the meaning of Christ's peace and rest.
"Come unto me, all ye that labour and are heavy laden, and I will give you rest."
Ellen White directly references Matthew 11:28 in this passage.
"We are in a world of suffering. Difficulty, trial, and sorrow await us all along the way to the heavenly home. But there are many who make life's burdens doubly heavy by continually anticipating trouble. If they meet with adversity or disappointment they think that everything is going to ruin, that theirs is the hardest lot of all, that they are surely coming to want. Thus they bring wretchedness upon themselves and cast a shadow upon all around them. Life itself becomes a burden to them. But it need not be thus. It will cost a determined effort to change the current of their thought. But the change can be made. Their happiness, both for this life and for the life to come, depends upon their fixing their minds upon cheerful things. Let them look away from the dark picture, which is imaginary, to the benefits which God has strewn in their pathway, and beyond these to the unseen and eternal. MH 247.3"
"These things I have spoken unto you, that in me ye might have peace. In the world ye shall have tribulation: but be of good cheer; I have overcome the world."
Both passages acknowledge the presence of tribulation in the world, but encourage a positive outlook and finding peace/cheer despite difficulties. The EGW passage provides practical advice on how to overcome negative thoughts and focus on God's blessings.