Professionally, both are legal scholars and important public officers. More is a principled and God-fearing man. This is seen when he refuses to give public approval to Henry's marriage with Anne Boleyn. He also refuses to accept bribe. At home, he is a good family man.
Cromwell, on the other hand, has no moral scruples and will do anything for position and money. These contrasting aspects of their characters are played out in the drama. For example, Cromwell's lack of moral scruples makes him a willing tool in the hands of the King. To satisfy the King's desire to remarry (which More is opposed to), he viciously implicates More in the bribery scandal and gets him executed in the end.
One other area where More and Cromwell contrast in character is the way they view friendship. While More is sincere and willing to help for a good cause, Cromwell is not. For example, more befriends Rich to improve the young man's moral and career development while Cromwell's friendship with Rich is exploitative and geared towards the acquisition of power, influence and money.
Judging from More's character as it develops in the play, one may consider him as naive even when he stands in great danger of his life and has virtually all his family opposing him. But More lives and dies for his principles. Cromwell, on the other hand, stands on no higher moral ground than his own material comfort which he pursues, vengefully.