Musar su Salmi 89:28

The purpose of the Passover sacrifice is first and foremost to demonstrate G–d's superiority over all other deities both in Heaven and on earth. This is important; G–d had endowed many agents with different powers, and the impression that there were a number of primary sources of power in the universe had to be refuted. The discrediting of the strongest of these forces, the שר של מצרים, automatically brought about the discrediting of all other deities.

Therein lies the secret of why the Priest must not perform the duties of the Levite, or vice versa. The Priests are the more important ones, their position vis-a-vis the Levites is like that of the firstborn in an ordinary family. The word בכור, firstborn, carries the connotation of גדולה, greatness, distinction, as we know from "אף אני בכור אתהו," "I too will appoint him as firstborn, highest of the kings of the earth" (Psalms 89,28). To signify that they occupied this position, they were awarded the firstborn of the pure animals born to the other tribes. This is also why the silver for redeeming the firstborn sons was awarded to them. The Levites were the "redemption" for the firstborn Israelites in accordance with their number.