The writers of the OT and NT never seem concerned to press that humans are greater than angels. There are various distinctions between humans and angels to be sure, but the concern never seems to be comparative.

Jonathan Edwards gave three reasons he understood humans to be greater than angels

1. Angels were made to serve God by serving man, but man was made to serve God directly.
2. Human grace, holiness, and love are greater virtues than angelic wisdom and strength.
3. Believers are united to Christ in a way angels never will be.

His basic reason was this, “Men are a more ultimate end of the creation than the angels.” Edwards’ point is logical, but I’m not aware of a single place in Scripture where an author is concerned to make this point. (Miscellanies #103)

Actually, reflecting on the way the Bible speaks of angels, it seems obvious that in many ways angels are greater than humans.

1. Angels are spirit, existing in a realm above us (Heb 1:14)
2. Angels worship around the throne, they participate in heavenly realities beyond our currently experience
3. Angels rescue humans (e.g. Lot, Peter), they have powers and abilities humans do not have

Moses portrays man as the pinnacle of God’s creative work, the bearers of his image (Gen 1). Yet angels are in a realm above us experiencing realities beyond us having powers that exceed ours.

Therefore, we should probably simply maintain that humans and angles hold distinct roles in the redemptive plan of God. Humans are the object of God’s redemptive plan, angels are the messengers and servants of the plan.

But to say in an absolute sense that angels are greater than humans, or that humans are greater than angels seems unwarranted in light of the Biblical evidence.