Is closing the eyes during prayer considered a distraction, and is it the distraction referred to in the saying: "To one better than me?"

The hadith mentioned in the question: "When a man stands for prayer, Allah turns His Face towards him. If he turns away, He says: 'O son of Adam, to whom are you turning? To one better for you than Me? Turn back!' If he turns away a second time, He says the same. If he turns away a third time, Allah Almighty turns His Face away from him," is unanimously considered weak.

It is authentically reported from Aisha (may Allah be pleased with her) that the Prophet (peace be upon him) said regarding turning away in prayer: "It is a snatching that Shaytan snatches from the prayer of a servant." This indicates its dislikeability, and the majority of scholars interpreted it as turning that does not reach the extent of turning one's chest away from the qiblah; otherwise, it would invalidate the prayer.

As for closing one's eyes during prayer, it is not considered turning away, and no authentic hadith from the Prophet (peace be upon him) prohibits it. However, some early Muslims disliked it, and a weak hadith has been reported concerning it.