John Calvin Commentary Hebrews 8:6

"But now hath he obtained a ministry the more excellent, by so much as he is also the mediator of a better covenant, which hath been enacted upon better promises." — Hebrews 8:6 (ASV)

But now has he obtained a more excellent ministry, etc. As he had previously inferred the excellence of the covenant from the dignity of the priesthood, so now he also maintains that Christ’s priesthood is more excellent than that of Aaron, because he is the interpreter and Mediator of a better covenant. Both were necessary, for the Jews needed to be led away from the superstitious observance of rituals, which prevented them from advancing directly toward attaining the real and pure truth of the Gospel. The Apostle now says that it was only right that Moses and Aaron should give way to Christ as to one who is more excellent, because the gospel is a more excellent covenant than the Law, and also because the death of Christ was a nobler sacrifice than the victims under the Law.

But what he adds is not without some difficulty — that the covenant of the Gospel was proclaimed on better promises. For it is certain that the fathers who lived under the Law had the same hope of eternal life set before them, just as we do. Since they had the grace of adoption in common with us, their faith must have rested on the same promises. But the comparison made by the Apostle refers to the form rather than to the substance; for though God promised them the same salvation which he promises us today, yet neither the manner nor the character of the revelation is the same as, or equal to, what we enjoy. If anyone wishes to know more on this subject, let him read Galatians chapters 4 and 5 and my Institutes.