Hawthorne paints an ugly picture of human nature in "Young Goodman Brown" by showing a large number of humans revealing their true natures at a devil-worshiping orgy in the forest. He only implies the evil in human nature in "The Minister''s Black Veil" by having a single character, the Reverend Mr. Clark, covering his face with a black veil to demonstrate that he has a dark side to his nature which he keeps hidden, and by implication to accuse all his parishioners of being just as bad, or worse. This makes all his parishioners realize that they too are hiding their wickedness and should also be wearing black veils. In other words, Hawthorne is saying the same thing in both stories but saying it in two different ways--one by showing everybody with their veils and the other by showing everybody except the minister without their veils. As stated in the Summary for "The Minister's Black Veil" in enotes Study Guide:
In “The Minister’s Black Veil,” Hawthorne presents another variation on his favorite theme: that humankind is universally afflicted with the so-called seven deadly sins (pride, covetousness, lust, envy, gluttony, anger, and sloth).
It seems to me that it would be fairly easy to write a compare-and-contrast essay about these two stories. They are the same because they both illustrate Hawthorne's favorite theme (which you could paraphrase from the above quote, especially about the seven deadly sins). They are different because in "Young Goodman Brown" Hawthorne shows human nature while in "The Minister's Black Veil" he hides human nature and lets the reader imagine what is hidden.
Such literary versatility is a sign of Hawthorne's genius. He was an extremely meticulous and conscientious writer. He spent twelve years teaching himself to write after graduating from Bowdoin College in 1825.