In my opinion, both "The Pardoner's Tale" and "The Nun's Priest's Tale" are very effective in providing a moralistic message to the audience of pilgrims gathered to listen.
There are arguments that would support that each tale is equally powerful, but I believe that although I personally prefer the story of Chanticleer, the rooster, it is probably the tale of the three drunkards who go looking for Death that has more of an impact.
"The Nun's Priest's Tale" is entertaining—even funny. And its message is very clear regarding pride. The Priest has been asked to tell a tale a little more uplifting than the one shared before his, "The Monk's Tale," which conveyed too many tragedies; ironically, however, the Priest also shares a story about the fall of Chanticleer.
The pilgrims have just listened to “The Monk’s Tale,” actually a series of short de casibustragedies, which medieval critical theory defined simply as the accounts of the fall of persons from high places.
However, it does not fill the reader with the same sense of doom and fear that "The Pardoner's Tale" does. The Pardoner tells a story of greed among three drunken men. They decide, after the passing of a friend, to pursue Death (personified as the entity that has taken the life of their friend). They are fired up, disrespectful of an old man (who may have symbolic significance of his own), and decide, upon discovering a hoard of gold, to murder one and steal his portion. The third also plots to murder the other two and steal their portion. In the end, all three die because of their greed.
This tale is probably more impactful because it directly relates to the sin of greed, of which the Pardoner has already confessed. Whereas Chanticleer's pride almost led to his death, he is spared at the last minute. However, the men who search for Death, find "him" in no uncertain terms, and it would seem this message is more powerful to the listener, in my opinion.