The whole book of Hebrews deals with the ways that the New Covenant in Christ is better than the Old Covenant and the Law given by Moses. A few points from Hebrews will serve to illustrate why Jesus’ sacrifice is better than the Levitical sacrifices.
The Levitical priests became priests simply because of their lineage—they were born into the priestly line. Jesus, however, was chosen by God to be a priest because of His personal qualifications (Hebrews 7:11–22).
There were many Levitical priests because they kept dying and had to be replaced. Jesus, however, lives forever and will continue to serve as priest forever, never being replaced (Hebrews 7:23–25).
The Levitical priests had to first offer sacrifices for their own sins and then for the sins of the people. Jesus had no sin and did not need to offer a sacrifice for Himself (Hebrews 7:26–27).
The Levitical priests served in an earthly setting, whereas Jesus ministers in a heavenly setting (Hebrews 8:1–5).
The Levitical priests ministered under the Old Covenant, whereas Jesus ministers under a New Covenant. The fact that God replaced the Old with the New is evidence that the New is better and that the Old must have had some deficiencies (Hebrews 8:6–13).
The Levitical priests entered the earthly Most Holy Place only once per year with the blood of an animal sacrifice. Jesus entered the heavenly Most Holy Place with the sacrifice of His own blood, and He is still there ministering on our behalf (Hebrews 9:11–24).
The Levitical priests had to make sacrifices repeatedly. This demonstrates the inherent weakness of their sacrifices. Jesus made one sacrifice for all sins for all people for all time. The Levitical sacrifices were merely imperfect pointers to Christ’s ultimate sacrifice. If they had been adequate in themselves, they would not have been repeated. It is impossible for the blood of bulls and goats to really take away sin (Hebrews 9:25—10:4).
In summary, “Day after day every priest stands and performs his religious duties; again and again he offers the same sacrifices, which can never take away sins. But when this priest had offered for all time one sacrifice for sins, he sat down at the right hand of God, and since that time he waits for his enemies to be made his footstool. For by one sacrifice he has made perfect forever those who are being made holy” (Hebrews 10:11–14).
Even after the Levitical priests had made the sacrifice, the way into the Most Holy Place was still barred. The high priest could only go in once per year, and other priests and the people at large could never go in. However, because of the sacrifice of Christ, “we have confidence to enter the Most Holy Place by the blood of Jesus, by a new and living way opened for us through the curtain, that is, his body” (Hebrews 10:19–20). The gospels record that at the death of Jesus the curtain in the temple was torn from top to bottom (Matthew 27:51), signifying that people could have direct access to God.
In short, the sacrifice of Jesus is better than the Levitical sacrifices because Jesus’ sacrifice did what the Levitical sacrifices could never do—make forgiveness of sins possible, once and for all, with a sacrifice that is never to be repeated.