When I research on the Catholic Priesthood, many apologists and theologians will make comparisons between Israelite priests and Catholic priests, especially in reference to the Pope guiding the church.
What are the significant differences in role and authority between the Israelite priesthood and the Catholic priesthood?
the priesthood of the [Old] Law was a figure of the priesthood of Christ, not as adequately representing the reality, but as falling far short thereof: both because the priesthood of the Law did not wash away sins, and because it was not eternal, as the priesthood of Christ. Now the excellence of Christ's over the Levitical priesthood was foreshadowed in the priesthood of Melchisedech, who received tithes from Abraham, in whose loins the priesthood of the Law was tithed. Consequently the priesthood of Christ is said to be "according to the order of Melchisedech" (Ps. 109:4), on account of the excellence of the true priesthood over the figural priesthood of the Law.