A.W. Pink sums up the comparison between Mt. Sinai and the Sermon on the Mount:

“Christ preached this sermon, which was an exposition of the Law, upon a mountain, because upon a mountain the Law was given…but observe the difference: when the Law was given (in the OT) the Lord came down upon the Mountain, now the Lord ‘went up’ into one; then He spoke in thunder and lightning, now in a still small voice; then the people were ordered to keep their distance, now they are invited to draw near- a blessed change!”

What we have here in the Sermon on the Mount is a Word from above…a Word from God. Moses met with God, received the Old Covenant, and delivered it to the Israelites in advance of their entering the Promise Land. In Matthew 5, Jesus, who is God, has invited us near in order to deliver the New Covenant in advance of our entering into the consummated Kingdom of Heaven.