In "Letter from Birmingham Jail," what are the differences in writing style between Martin Luther King and the clergymen?
I assume that when you say "the clergymen" you are talking about those who signed the letter called "A Call for Unity" which was the letter to which King is responding in his letter.
If this is the case, the clergymen write their letter in a much more formal, dry, and impersonal style whereas King writes his in a style that is both less formal and more (at times) like a sermon. King's letter is by far the more passionate.
The clergymen's letter reads like a legal argument in a way. It has no emotion in the writing. It talks about things like "increased forbearance" and it talks about how responsible citizens have "undertaken to work" on fixing the problems of the community. It sounds very antiseptic, albeit very educated.
By contrast, King's letter is personal and emotional. He uses the first person a lot. He uses plain language much of the time, saying things like "I am in Birmingham because injustice is here." Later on, he starts to let his rhetoric flow as if the letter were a sermon. He uses colorful language, saying things like
As in so many past experiences, our hopes had been blasted, and the shadow of deep disappointment settled upon us.
In these ways, King's letter comes across as much, much, more passionate and personal than the rather blandly written letter of the clergymen.