What are the differences in manner between Judge Hathorne and Danforth?
Danforth seems secure in himself, his authority, and the court; he is the deputy governor of the colony, after all, so he really has nothing to prove to the inhabitants of Salem. He is calm and collected, and he rests confidently on his wealth of experience. He tells Francis Nurse, "near to four hundred are in the jails from Marblehead to Lynn [...] upon my signature" and "seventy-two [are] condemned to hang by that signature." Danforth has many trials under his belt, and he thinks that Salem is just like any other town, these trials just like all the others. He is self-assured and collected.
Hathorne, on the other hand, seems to feel less secure in his position. Toward the beginning of Act Three, he calls Giles Corey foolish for "roarin'" into the court with evidence he believes will clear his wife. Giles retorts, "You're not a Boston judge yet, Hathorne. You'll not call me daft!" Thus, we can see that Hathorne is really not as respected as Danforth, which may account for some of his insecurity. Further, he plays games with the accused in a way that Danforth never does. When he questions Martha Corey, Giles's wife, he asks her if she denies that she is a witch. She does, and says, "I know not what a witch is." He responds in a rather snide way, "How do you know, then, that you are not a witch?" He knows what she meant: that she's not a witch and has never met one and therefore cannot say with certainty what a witch is even like. However, he purposely misinterprets her statement so that he can appear to catch her out. It's a rather childish and immature way to question someone, and we never see Danforth question someone in this tricky way.
There is not much in way of specific differences in both judges. Yet, one of the most striking is how they both seem to approach the questioning of their power. Hathorne does not take real well to anyone who should question the procedures of the court. The testy exchange between he and Corey is evidence of this. There is some level of personal animosity between them, something that Corey thinks will be absent because of his own background with Danforth's father. Yet, while there is a personal element to Hathorne, Danforth sincerely believes, or purports to believe, that the questioning of the court is not an attack on him as much as it is on the legal condition of the trials, in general. Danforth continually grills Proctor on his desire to bring down the court. Proctor, for his part, simply wishes to clear his name and focus the trials on their weak evidential nature. Yet, Danforth successfully goads Proctor into admitting that there is another motivation in his questioning. In this, Danforth is shown to be more concerned with the overall nature of the court, something into which he has absorbed his own identity, making him slightly different than Hathorne in this respect.