Adam Clarke on Hebrews 8:6

Now hath he obtained a more excellent ministry - His office of priesthood is more excellent than the Levitical, because the covenant is better, and established on better promises: the old covenant referred to earthly things; the new covenant, to heavenly. The old covenant had promises of secular good; the new covenant, of spiritual and eternal blessings. As far as Christianity is preferable to Judaism, as far as Christ is preferable to Moses, as far as spiritual blessings are preferable to earthly blessings, and as far as the enjoyment of God throughout eternity is preferable to the communication of earthly good during time; so far does the new covenant exceed the old.