Christ's priesthood preceded that of the Levites. Even Levi gave tithes to Melchizedek through Abraham (Heb.7:9-10)
He being God incarnated as Man is the only perfect Mediator (1Tim.2:5, Heb.2:9,10,14)
The levites could not be permanent because they died, but Jesus lives for ever and has a permanent priesthood (Heb. 7:23-24)
The levites had to offer sacrifices for their own sins, but Christ is the sinless and perfect High Priest of God (Heb.7:26-27)
The levites served in a man made tabernacle, but He entered into the heavenly one, not made with human hands (Heb.8:5; 9:11)
Sacrifices were necessary to purify the copies of heavenly things on earth (tabernacle and instruments), but the heavenly things could only be purified with a better sacrifice, i.e. of Jesus (Heb.9:23)
The OT ceremonies were only temporary, till Jesus came (Heb.9:10)
The OT ceremonies were only external, but Christ works within us (Heb.9:10)
The levites offered blood of animals; but Jesus offered Himself (Heb.9:11-14)
The levites had to sacrifice many times, but Jesus offered Himself once for all (Heb.7:27)
Jesus is the Mediator of a superior and new covenant that is established on better promises (Heb.8:6, 10-12) (2Cor.3:7-11)
The old covenant is made obsolete by the new covenant (Heb.8:13)
The blood of Jesus cleanses our conscience to serve the living God (Heb.9:9,14)
