"Aside from the joy that John found in his mission, his life had been one of sorrow. His voice had been seldom heard except in the wilderness. His was a lonely lot. And he was not permitted to see the result of his own labors. It was not his privilege to be with Christ and witness the manifestation of divine power attending the greater light. It was not for him to see the blind restored to sight, the sick healed, and the dead raised to life. He did not behold the light that shone through every word of Christ, shedding glory upon the promises of prophecy. The least disciple who saw Christ's mighty works and heard His words was in this sense more highly privileged than John the Baptist, and therefore is said to have been greater than he. DA 220.3"
"Verily I say unto you, Among them that are born of women there hath not risen a greater than John the Baptist: notwithstanding he that is least in the kingdom of heaven is greater than he."
EGW explains the meaning of Matthew 11:11, elaborating on the idea that even the least in the kingdom of heaven is greater than John because they witnessed Christ's ministry, which John did not.
"Through the vast throngs that had listened to John's preaching, his fame had spread throughout the land. A deep interest was felt as to the result of his imprisonment. Yet his blameless life, and the strong public sentiment in his favor, led to the belief that no violent measures would be taken against him. DA 220.4"
"And when he would have put him to death, he feared the multitude, because they counted him as a prophet."
Both passages discuss Herod's hesitation to kill John due to public opinion.
"Herod believed John to be a prophet of God, and he fully intended to set him at liberty. But he delayed his purpose from fear of Herodias. DA 220.5"
"For Herod feared John, knowing that he was a just man and an holy, and observed him; and when he heard him, he did many things, and heard him gladly."
Both passages discuss Herod's fear of John and his initial inclination to release him.