How do we know Christ's ministry is superior?

The superiority of Christ's ministry is demonstrated through its fulfillment of the law and the new covenant it brings. The previous ministrations outlined in the Old Testament highlighted the inability of the law to save. Instead, Christ's ministry 'now' introduces a better thing that provides for the complete and perfect salvation of His elect. Hebrews 8 discusses this transformative work and indicates that what the law could not accomplish, Christ has achieved through His death and resurrection, delivering us from sin and death once and for all.