The main differences between the two characters are that Mrs. Barrows is female and aggressive, while Mr. Martin is male and both passive and defensive. Related to the latter are that she is outspoken and straightforward, to the point of offensive. Mr. Martin is introverted and secretive, so much so that no one suspects him of being manipulative.
Because Mrs. Barrows looks before she leaps, she does not spend time assessing her situation, much less understanding other peoples' personalities or motivations. Mr. Martin, in contrast, sits back and assesses the situation. By taking the time and figuring out what makes others tick, Mr. Martin in the long run makes more careful decisions.
That he might have a devious side occurs neither to her or to his boss, so Martin successfully pulls off his coup.