Tom uses his money as a moral excuse. He is not called upon to act morally because he comes from money. Money insulates him.
Gatsby's money is a tool and a mask, but not a moral one. Gatsby acquires his wealth in order to "acquire" Daisy. His money is new, purposeful, and not to be taken for granted.
Take a look at the character analysis here at enotes:
To write an essay comparing Tom and Gatsby, you'd want to start by listing all their major characteristics and actions in the novel. Then you'd look for categories where they can be compared and areas where they differ.
You could start with some of the basics: both male, both rich, both in love (or at least involved) with Daisy. You'd then move on to more complicated distinctions. For example, Tom's money is old money, while Gatsby's is new.
You'd look at their characters, and, ideally, at their relative guilt and innocence in the novel. Do they get the endings they deserve? You'd want to look at what the novel tells us by this ending, and to reach a decision there.
You might also want to check out the eNotes free guide called How to Write a Compare-and-Contrast Essay.