The difference between the passive nature of Godfrey and that of Silas is based on the reason behind their behaviors.
Godfrey is a good-natured individual, however, he lacks character. In fact this is his biggest flaw. He tends to fall for his weaknesses, such as alcohol, women, and pleasure, which leads him to marry a woman who is an opium fiend and, to top it all, they have a child together.
Godfrey also seems to be submissive to his younger brother, Dunstan. The latter is a very malicious man who thinks of nobody but himself and keeps Godfrey threatened by telling him that he will disclose the secret of his hidden wife and child.
Comparatively, Silas is also a good-natured man. He seems to automatically offer his help to others, and it is his good nature what makes others take advantage of him and betray him at Lantern Yard.
One interesting point to make is that Silas, even after theft of his gold in Raveloe and all that comes along with it, still manages to accept the event and learn from the experience. This shows the strength of his character, and the level of dignity that he has. This may be the biggest difference between he and Godfrey's behavior: Although they are both good men by nature, Silas shows a type of resilience that is not evident in Godfrey.