"The interest of the people in Christ and His work had steadily increased. They were charmed with His teaching, but they were also greatly perplexed. They had respected the priests and rabbis for their intelligence and apparent piety. In all religious matters they had ever yielded implicit obedience to their authority. Yet they now saw these men trying to cast discredit upon Jesus, a teacher whose virtue and knowledge shone forth the brighter from every assault. They looked upon the lowering countenances of the priests and elders, and there saw discomfiture and confusion. They marveled that the rulers would not believe on Jesus, when His teachings were so plain and simple. They themselves knew not what course to take. With eager anxiety they watched the movements of those whose counsel they had always followed. DA 611.1"
"For he taught them as one having authority, and not as the scribes."
Both passages highlight the contrast between Jesus' teaching style and the scribes/priests, and the people's reaction to it. The EGW passage elaborates on the perplexity and confusion of the people, which is a reasonable expansion of the idea presented in Matthew 7:29.
"The officers answered, Never man spake like this man."
Both passages describe the impact of Jesus' teaching on the people. John 7:46 focuses on the unique quality of His speech, while the EGW passage describes the people being charmed and perplexed, but both reflect the powerful effect Jesus had on His audience.
"In the parables which Christ had spoken, it was His purpose both to warn the rulers and to instruct the people who were willing to be taught. But there was need to speak yet more plainly. Through their reverence for tradition and their blind faith in a corrupt priesthood, the people were enslaved. These chains Christ must break. The character of the priests, rulers, and Pharisees must be more fully exposed. DA 611.2"
"But he answered and said unto them, Why do ye also transgress the commandment of God by your tradition?"
EGW directly addresses the issue of tradition superseding God's commandments, which is the core of Matthew 15:3. The EGW passage amplifies the principle found in the verse.
"Stand fast therefore in the liberty wherewith Christ hath made us free, and be not entangled again with the yoke of bondage."
Both passages discuss freedom from bondage. Galatians 5:1 speaks of freedom from the law, while EGW speaks of freedom from tradition and corrupt priesthood. The connection is thematic, focusing on the concept of liberation through Christ.